Difference between revisions of "Glossary of EM.Cube's Python Functions"

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|-
 
|-
 
| sign(x)
 
| sign(x)
 +
| Std. Python function
 
| Sign function
 
| Sign function
 
| 1 if x>0, -1 if x<0
 
| 1 if x>0, -1 if x<0
 
|-
 
|-
 
| fac(x)
 
| fac(x)
 +
| Std. Python function
 
| Factorial
 
| Factorial
 
| For integer values of x: n! = n(n-1)(n-2)...3.2.1
 
| For integer values of x: n! = n(n-1)(n-2)...3.2.1
 
|-
 
|-
 
| fac2(x)
 
| fac2(x)
 +
| Std. Python function
 
| Double factorial
 
| Double factorial
 
| For even integer values of x: n!! = n(n-2)(n-4)...4.2, for odd integer values of x: n!! = n(n-2)(n-4)...5.3
 
| For even integer values of x: n!! = n(n-2)(n-4)...4.2, for odd integer values of x: n!! = n(n-2)(n-4)...5.3
 
|-
 
|-
 
| ceiling(x)
 
| ceiling(x)
 +
| Std. Python function
 
| Ceiling function
 
| Ceiling function
 
| Nearest integer >= x
 
| Nearest integer >= x
Line 188: Line 192:
 
|-
 
|-
 
| Ci(x)
 
| Ci(x)
 +
| Std. Python function
 
| Cosine integral function
 
| Cosine integral function
 
| See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
 
|-
 
|-
 
| Si(x)
 
| Si(x)
 +
| Std. Python function
 
| Sine integral function
 
| Sine integral function
 
| See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Trigonometric_integral Trigonometric Integrals on Wikipedia.]
 
|-
 
|-
 
| C(x)
 
| C(x)
 +
| Std. Python function
 
| Cosine Fresnel integral function
 
| Cosine Fresnel integral function
 
| See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
 
|-
 
|-
 
| S(x)
 
| S(x)
 +
| Std. Python function
 
| Sine Fresnel integral function
 
| Sine Fresnel integral function
 
| See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Fresnel_integral Fresnel Integrals on Wikipedia.]
Line 205: Line 213:
 
|-
 
|-
 
| Ellip_E(x)
 
| Ellip_E(x)
 +
| Std. Python function
 
| Elliptic function of the first kind
 
| Elliptic function of the first kind
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
 
|-
 
|-
 
| Ellip_K(x)
 
| Ellip_K(x)
 +
| Std. Python function
 
| Elliptic function of the second kind
 
| Elliptic function of the second kind
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Elliptic_integral Elliptic Integrals on Wikipedia.]
Line 214: Line 224:
 
|-
 
|-
 
| Ei(x)
 
| Ei(x)
 +
| Std. Python function
 
| Exponential integral function
 
| Exponential integral function
 
| See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
 
|-
 
|-
 
| En(n,x)
 
| En(n,x)
 +
| Std. Python function
 
| Generalized exponential integral function of order n
 
| Generalized exponential integral function of order n
 
| See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Exponential_integral Exponential Integrals on Wikipedia.]
 
|-
 
|-
 
| gauss(x)
 
| gauss(x)
 +
| Std. Python function
 
| Gaussian function
 
| Gaussian function
 
| -
 
| -
 
|-
 
|-
 
| erf(x)
 
| erf(x)
 +
| Std. Python function
 
| Error function
 
| Error function
 
| See [https://en.wikipedia.org/wiki/Error_function Error Function on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Error_function Error Function on Wikipedia.]
 
|-
 
|-
 
| gamma(x)
 
| gamma(x)
 +
| Std. Python function
 
| Gamma function
 
| Gamma function
 
| See [https://en.wikipedia.org/wiki/Gamma_function Gamma Function on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Gamma_function Gamma Function on Wikipedia.]
 
|-
 
|-
 
| Airy_A(x)
 
| Airy_A(x)
 +
| Std. Python function
 
| Airy function of the first kind
 
| Airy function of the first kind
 
| See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
 
|-
 
|-
 
| Airy_B(x)
 
| Airy_B(x)
 +
| Std. Python function
 
| Airy function of the second kind
 
| Airy function of the second kind
 
| See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Airy_function Airy Functions on Wikipedia.]
 
|-
 
|-
 
| Jn(n,x)
 
| Jn(n,x)
 +
| Std. Python function
 
| Bessel function of the first kind and order n
 
| Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| Yn(n,x)
 
| Yn(n,x)
 +
| Std. Python function
 
| Bessel function of the second kind and order n
 
| Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| In(n,x)
 
| In(n,x)
 +
| Std. Python function
 
| Modified Bessel function of the first kind and order n
 
| Modified Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| Kn(n,x)
 
| Kn(n,x)
 +
| Std. Python function
 
| Modified Bessel function of the second kind and order n
 
| Modified Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| SB_jn(n,x)
 
| SB_jn(n,x)
 +
| Std. Python function
 
| Spherical Bessel function of the first kind and order n
 
| Spherical Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| SB_yn(n,x)
 
| SB_yn(n,x)
 +
| Std. Python function
 
| Spherical Bessel function of the second kind and order n
 
| Spherical Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| SB_in(n,x)
 
| SB_in(n,x)
 +
| Std. Python function
 
| Modified spherical Bessel function of the first kind and order n
 
| Modified spherical Bessel function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| SB_kn(n,x)
 
| SB_kn(n,x)
 +
| Std. Python function
 
| Modified spherical Bessel function of the second kind and order n
 
| Modified spherical Bessel function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Bessel_function Bessel Functions on Wikipedia.]
 
|-
 
|-
 
| Pn(n,x)
 
| Pn(n,x)
 +
| Std. Python function
 
| Legendre function of the first kind and order n
 
| Legendre function of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomial Legendre Polynomials on Wikipedia.]
 
|-
 
|-
 
| Qn(n,x)
 
| Qn(n,x)
 +
| Std. Python function
 
| Legendre function of the second kind and order n
 
| Legendre function of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Legendre_polynomials Legendre Polynomials on Wikipedia.]
 
|-
 
|-
 
| Tn(n,x)
 
| Tn(n,x)
 +
| Std. Python function
 
| Chebyshev polynomial of the first kind and order n
 
| Chebyshev polynomial of the first kind and order n
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
|-
 
|-
 
| Un(n,x)
 
| Un(n,x)
 +
| Std. Python function
 
| Chebyshev polynomial of the second kind and order n
 
| Chebyshev polynomial of the second kind and order n
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev Polynomials on Wikipedia.]
 
|-
 
|-
 
| LGn(n,x)
 
| LGn(n,x)
 +
| Std. Python function
 
| Laguerre polynomial of order n
 
| Laguerre polynomial of order n
 
| See [https://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre Polynomials on Wikipedia.]
 
|-
 
|-
 
| Hn(n,x)
 
| Hn(n,x)
 +
| Std. Python function
 
| Hermite polynomial of order n
 
| Hermite polynomial of order n
 
| See [https://en.wikipedia.org/wiki/Hermite_polynomials Hermite Polynomials on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Hermite_polynomials Hermite Polynomials on Wikipedia.]
 
|-
 
|-
 
| Un(n,x)
 
| Un(n,x)
 +
| Std. Python function
 
| Hermite-Gauss function of order n
 
| Hermite-Gauss function of order n
 
| -
 
| -
 
|-
 
|-
 
| Math_ce(n,r,x)
 
| Math_ce(n,r,x)
 +
| Std. Python function
 
| Even periodic (cosine) Mathieu function of order n
 
| Even periodic (cosine) Mathieu function of order n
 
| See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
 
|-
 
|-
 
| Math_se(n,r,x)
 
| Math_se(n,r,x)
 +
| Std. Python function
 
| Odd periodic (sine) Mathieu function of order n
 
| Odd periodic (sine) Mathieu function of order n
 
| See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
 
| See [https://en.wikipedia.org/wiki/Mathieu_function Mathieu Functions on Wikipedia.]
 
|-
 
|-
 
| Rect(x)
 
| Rect(x)
 +
| EMAG Python function
 
| Rectangle function
 
| Rectangle function
 
| 1 if |x|&le;0.5, 0 elsewhere  
 
| 1 if |x|&le;0.5, 0 elsewhere  
 
|-
 
|-
 
| Tri(x)
 
| Tri(x)
 +
| EMAG Python function
 
| Triangle function
 
| Triangle function
 
| 1 if |1-x|&le;1, 0 elsewhere  
 
| 1 if |1-x|&le;1, 0 elsewhere  
 
|-
 
|-
 
| Spln2(x)
 
| Spln2(x)
 +
| EMAG Python function
 
| Quadratic spline function
 
| Quadratic spline function
 
| -
 
| -
 
|-
 
|-
 
| Spln3(x)
 
| Spln3(x)
 +
| EMAG Python function
 
| Cubic spline function
 
| Cubic spline function
 
| -
 
| -
 
|-
 
|-
 
| Step(x)
 
| Step(x)
 +
| EMAG Python function
 
| Step function
 
| Step function
 
| 1 if x>0, 0 if x<0
 
| 1 if x>0, 0 if x<0
 
|-
 
|-
 
| Haar(x)
 
| Haar(x)
 +
| EMAG Python function
 
| Haar function
 
| Haar function
 
| sign(x) if |x|<0.5, 0 elsewhere
 
| sign(x) if |x|<0.5, 0 elsewhere
 
|-
 
|-
 
| Ramp(x)
 
| Ramp(x)
 +
| EMAG Python function
 
| Ramp function
 
| Ramp function
 
| -
 
| -
 
|-
 
|-
 
| Trapz(a,x)
 
| Trapz(a,x)
 +
| EMAG Python function
 
| Trapezoidal function
 
| Trapezoidal function
 
| -
 
| -
 
|-
 
|-
 
| Sqwv(x)
 
| Sqwv(x)
 +
| EMAG Python function
 
| Square wave function
 
| Square wave function
 
| -
 
| -
 
|-
 
|-
 
| Stwv(x)
 
| Stwv(x)
 +
| EMAG Python function
 
| Sawtooth wave function
 
| Sawtooth wave function
 
| -
 
| -
 
|-
 
|-
 
| Trwv(x)
 
| Trwv(x)
 +
| EMAG Python function
 
| Triangle wave function
 
| Triangle wave function
 
| -
 
| -
 
|-
 
|-
 
| Plstr(d,x)
 
| Plstr(d,x)
 +
| EMAG Python function
 
| Pulse train function with duty cycle d
 
| Pulse train function with duty cycle d
 
| -
 
| -
 
|-
 
|-
 
| Sinc(d,x)
 
| Sinc(d,x)
 +
| EMAG Python function
 
| Sinc function
 
| Sinc function
 
| sin(pi*x)/(pi*x)
 
| sin(pi*x)/(pi*x)
 
|-
 
|-
 
| Fejer(n,x)
 
| Fejer(n,x)
 +
| EMAG Python function
 
| Fejer function of order n
 
| Fejer function of order n
 
| -
 
| -
 
|-
 
|-
 
| Rand(x)
 
| Rand(x)
 +
| EMAG Python function
 
| Random function
 
| Random function
 
| -
 
| -
−
|-
 
−
| Fltr_B(n,x)
 
−
| Butterworth filter function of order n
 
−
| -
 
−
|-
 
−
| Fltr_CH1(n,e,x)
 
−
| Chebyshev filter function of the first kind, order n
 
−
| e: ripple factor e
 
−
|-
 
−
| Fltr_CH2(n,e,x)
 
−
| Chebyshev filter function of the second kind, order n
 
−
| e: ripple factor e
 
−
|-
 
−
| Fltr_E(n,s,e,x)
 
−
| Elliptic filter function of order n
 
−
| s: selectivity factor s, ripple factor e, n = 0, 1, 2, 3, 4, 6, 8, 9, 12
 
 
|-
 
|-
 
| Z0_MS(e,x)
 
| Z0_MS(e,x)
 +
| EMAG Python function
 
| Characteristic impedance of a microstrip transmission line  
 
| Characteristic impedance of a microstrip transmission line  
 
| x: width-to-height ratio, e: substrate permittivity
 
| x: width-to-height ratio, e: substrate permittivity
 
|-
 
|-
 
| w_MS(z,e,t)
 
| w_MS(z,e,t)
 +
| EMAG Python function
 
| Width of a microstrip transmission line   
 
| Width of a microstrip transmission line   
 
| z: characteristic impedance, e: substrate permittivity, t: substrate thickness
 
| z: characteristic impedance, e: substrate permittivity, t: substrate thickness
 
|-
 
|-
 
| eeff_MS(e,x)
 
| eeff_MS(e,x)
 +
| EMAG Python function
 
| Effective permittivity of a microstrip transmission line
 
| Effective permittivity of a microstrip transmission line
 
| x: width-to-height ratio, e: substrate permittivity
 
| x: width-to-height ratio, e: substrate permittivity
 
|-
 
|-
 
| woh_MS(e,z)
 
| woh_MS(e,z)
 +
| EMAG Python function
 
| Width-to-height ratio of a microstrip transmission line  
 
| Width-to-height ratio of a microstrip transmission line  
 
| z: characteristic impedance z, e: substrate permittivity
 
| z: characteristic impedance z, e: substrate permittivity
 
|-
 
|-
 
| Z0_CPW(e,x,y)
 
| Z0_CPW(e,x,y)
 +
| EMAG Python function
 
| Characteristic impedance of a coplanar waveguide transmission line  
 
| Characteristic impedance of a coplanar waveguide transmission line  
 
| x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
 
| x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
 
|-
 
|-
 
| eeff_CPW(e,x,y)
 
| eeff_CPW(e,x,y)
 +
| EMAG Python function
 
| Effective permittivity of a coplanar waveguide transmission line   
 
| Effective permittivity of a coplanar waveguide transmission line   
 
| x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
 
| x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
 
|-
 
|-
 
| horn_a(d,x,y)
 
| horn_a(d,x,y)
 +
| EMAG Python function
 
| Wavelength-normalized a-dimension of an optimal pyramidal horn antenna   
 
| Wavelength-normalized a-dimension of an optimal pyramidal horn antenna   
 
| d: directivity d, x and y: wavelength-normalized waveguide dimensions
 
| d: directivity d, x and y: wavelength-normalized waveguide dimensions
 
|-
 
|-
 
| horn_b(d,x,y)
 
| horn_b(d,x,y)
 +
| EMAG Python function
 
| Wavelength-normalized b-dimension of an optimal pyramidal horn antenna   
 
| Wavelength-normalized b-dimension of an optimal pyramidal horn antenna   
 
| d: directivity d, x and y: wavelength-normalized waveguide dimensions
 
| d: directivity d, x and y: wavelength-normalized waveguide dimensions
 
|-
 
|-
 
| horn_l(d,x,y)
 
| horn_l(d,x,y)
 +
| EMAG Python function
 
| Wavelength-normalized length of an optimal pyramidal horn antenna   
 
| Wavelength-normalized length of an optimal pyramidal horn antenna   
 
| d: directivity d, x and y: wavelength-normalized waveguide dimensions
 
| d: directivity d, x and y: wavelength-normalized waveguide dimensions

Revision as of 14:37, 29 August 2016

The table below gives a list of all the currently available library functions in EM.Cube:

Syntax Type Description Notes
sign(x) Std. Python function Sign function 1 if x>0, -1 if x<0
fac(x) Std. Python function Factorial For integer values of x: n! = n(n-1)(n-2)...3.2.1
fac2(x) Std. Python function Double factorial For even integer values of x: n!! = n(n-2)(n-4)...4.2, for odd integer values of x: n!! = n(n-2)(n-4)...5.3
ceiling(x) Std. Python function Ceiling function Nearest integer >= x
floor(x) Std. Python function Floor function Nearest integer <= x
power(x,y) Std. Python function Power function x**y
sqrt(x) Std. Python function Square root function x^(1/2)
exp(x) Std. Python function Exponential function e**x
log(x) Std. Python function Natural logarithm function -
log10(x) Std. Python function Base 10 logarithm function ln(x)/ln(10)
log(x,a) Std. Python function Base a logarithm function ln(x)/ln(a)
abs(x) Std. Python function Absolute value function x if x>0, -x if x<0
sin(x) Std. Python function Sine function -
cos(x) Std. Python function Cosine function -
tan(x) Std. Python function Tangent function -
sec(x) Std. Python function Secant function -
csc(x) Std. Python function Cosecant function -
cot(x) Std. Python function Cotangent function -
asin(x) Std. Python function Inverse sine function -
acos(x) Std. Python function Inverse cosine function -
atan(x) Std. Python function Inverse tangent function -
atan2(x,y) Inverse tangent function -
asec(x) Std. Python function Inverse secant function -
acsc(x) Std. Python function Inverse cosecant function -
acot(x) Std. Python function Inverse cotangent function -
sinh(x) Std. Python function Hyperbolic sine function -
cosh(x) Std. Python function Hyperbolic cosine function -
tanh(x) Std. Python function Hyperbolic tangent function -
sech(x) Std. Python function Hyperbolic secant function -
csch(x) Std. Python function Hyperbolic cosecant function -
coth(x) Std. Python function Hyperbolic cotangent function -
asinh(x) Std. Python function Inverse hyperbolic sine function -
acosh(x) Std. Python function Inverse hyperbolic cosine function -
atanh(x) Std. Python function Inverse hyperbolic tangent function -
asech(x) Std. Python function Inverse hyperbolic secant function -
acsch(x) Std. Python function Inverse hyperbolic cosecant function -
acoth(x) Std. Python function Inverse hyperbolic cotangent function -
Ci(x) Std. Python function Cosine integral function See Trigonometric Integrals on Wikipedia.
Si(x) Std. Python function Sine integral function See Trigonometric Integrals on Wikipedia.
C(x) Std. Python function Cosine Fresnel integral function See Fresnel Integrals on Wikipedia.
S(x) Std. Python function Sine Fresnel integral function See Fresnel Integrals on Wikipedia. -
Ellip_E(x) Std. Python function Elliptic function of the first kind See Elliptic Integrals on Wikipedia.
Ellip_K(x) Std. Python function Elliptic function of the second kind See Elliptic Integrals on Wikipedia. -
Ei(x) Std. Python function Exponential integral function See Exponential Integrals on Wikipedia.
En(n,x) Std. Python function Generalized exponential integral function of order n See Exponential Integrals on Wikipedia.
gauss(x) Std. Python function Gaussian function -
erf(x) Std. Python function Error function See Error Function on Wikipedia.
gamma(x) Std. Python function Gamma function See Gamma Function on Wikipedia.
Airy_A(x) Std. Python function Airy function of the first kind See Airy Functions on Wikipedia.
Airy_B(x) Std. Python function Airy function of the second kind See Airy Functions on Wikipedia.
Jn(n,x) Std. Python function Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
Yn(n,x) Std. Python function Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
In(n,x) Std. Python function Modified Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
Kn(n,x) Std. Python function Modified Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
SB_jn(n,x) Std. Python function Spherical Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
SB_yn(n,x) Std. Python function Spherical Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
SB_in(n,x) Std. Python function Modified spherical Bessel function of the first kind and order n See Bessel Functions on Wikipedia.
SB_kn(n,x) Std. Python function Modified spherical Bessel function of the second kind and order n See Bessel Functions on Wikipedia.
Pn(n,x) Std. Python function Legendre function of the first kind and order n See Legendre Polynomials on Wikipedia.
Qn(n,x) Std. Python function Legendre function of the second kind and order n See Legendre Polynomials on Wikipedia.
Tn(n,x) Std. Python function Chebyshev polynomial of the first kind and order n See Chebyshev Polynomials on Wikipedia.
Un(n,x) Std. Python function Chebyshev polynomial of the second kind and order n See Chebyshev Polynomials on Wikipedia.
LGn(n,x) Std. Python function Laguerre polynomial of order n See Laguerre Polynomials on Wikipedia.
Hn(n,x) Std. Python function Hermite polynomial of order n See Hermite Polynomials on Wikipedia.
Un(n,x) Std. Python function Hermite-Gauss function of order n -
Math_ce(n,r,x) Std. Python function Even periodic (cosine) Mathieu function of order n See Mathieu Functions on Wikipedia.
Math_se(n,r,x) Std. Python function Odd periodic (sine) Mathieu function of order n See Mathieu Functions on Wikipedia.
Rect(x) EMAG Python function Rectangle function x|≤0.5, 0 elsewhere
Tri(x) EMAG Python function Triangle function 1-x|≤1, 0 elsewhere
Spln2(x) EMAG Python function Quadratic spline function -
Spln3(x) EMAG Python function Cubic spline function -
Step(x) EMAG Python function Step function 1 if x>0, 0 if x<0
Haar(x) EMAG Python function Haar function x|<0.5, 0 elsewhere
Ramp(x) EMAG Python function Ramp function -
Trapz(a,x) EMAG Python function Trapezoidal function -
Sqwv(x) EMAG Python function Square wave function -
Stwv(x) EMAG Python function Sawtooth wave function -
Trwv(x) EMAG Python function Triangle wave function -
Plstr(d,x) EMAG Python function Pulse train function with duty cycle d -
Sinc(d,x) EMAG Python function Sinc function sin(pi*x)/(pi*x)
Fejer(n,x) EMAG Python function Fejer function of order n -
Rand(x) EMAG Python function Random function -
Z0_MS(e,x) EMAG Python function Characteristic impedance of a microstrip transmission line x: width-to-height ratio, e: substrate permittivity
w_MS(z,e,t) EMAG Python function Width of a microstrip transmission line z: characteristic impedance, e: substrate permittivity, t: substrate thickness
eeff_MS(e,x) EMAG Python function Effective permittivity of a microstrip transmission line x: width-to-height ratio, e: substrate permittivity
woh_MS(e,z) EMAG Python function Width-to-height ratio of a microstrip transmission line z: characteristic impedance z, e: substrate permittivity
Z0_CPW(e,x,y) EMAG Python function Characteristic impedance of a coplanar waveguide transmission line x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
eeff_CPW(e,x,y) EMAG Python function Effective permittivity of a coplanar waveguide transmission line x: slot width-to-height ratio, y: center strip width-to-height ratio, e: substrate permittivity
horn_a(d,x,y) EMAG Python function Wavelength-normalized a-dimension of an optimal pyramidal horn antenna d: directivity d, x and y: wavelength-normalized waveguide dimensions
horn_b(d,x,y) EMAG Python function Wavelength-normalized b-dimension of an optimal pyramidal horn antenna d: directivity d, x and y: wavelength-normalized waveguide dimensions
horn_l(d,x,y) EMAG Python function Wavelength-normalized length of an optimal pyramidal horn antenna d: directivity d, x and y: wavelength-normalized waveguide dimensions

 

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