FewSpecialFunctions.ClausenFunction
Clausen(x, min_tol=1e-15)

Computes the Clausen function

`$math Cl_2(\phi) = - \int_0^\phi \log|2\sin(x/2)| dx `$

Returns $Cl_2(\phi)$.

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FewSpecialFunctions.Debye_functionFunction
Debye_function(n,x,min_tol=1e-15)

The Debye function(n,x) given by

\[ D_n(x) = \frac{n}{x^n} \int_0^x \frac{t^n}{e^{t}-1} dx\]

Returns the value $D(n,x)$

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Missing docstring.

Missing docstring for regular_Coulomb. Check Documenter's build log for details.

Missing docstring.

Missing docstring for irregular_Coulomb. Check Documenter's build log for details.

FewSpecialFunctions.CFunction
C(ℓ,η)

Returns Coulomb normalization constant given by

\[ C_\ell(\eta) = \frac{2^\ell \exp(-\pi \eta/2) |\Gamma(\ell+1+i \eta)|}{(2\ell+1)!}\]

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FewSpecialFunctions.θFunction
θ(ℓ,η,ρ)

Returns the phase of the Coulomb functions given by

\[ \theta_\ell(\eta,\rho) = \rho - \eta \ln(2\rho) - \frac{1}{2}\ell \pi + \sigma_\ell(\eta)\]

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FewSpecialFunctions.Coulomb_H_minusFunction
Coulomb_H_minus(ℓ,η,ρ)

Complex Coulomb wave function. Infinity handled using the substitution f(t) -> f(u/(1-u)*1/(1-u)^2). Returns Coulomb wave function

\[ H^{-}_\ell = G_\ell - iF_\ell\]

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FewSpecialFunctions.StruveFunction
Struve(ν,z,min_tol=1e-15)

Returns the Struve function given by

\[ \mathbf{H}_\nu(z) = \frac{2(z/2)^\nu}{\sqrt{\pi}\Gamma(\nu+1/2)} \int_0^1 (1-t)^{{\nu-1/2}}\sin(zt) \, \text{d}t\]

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FewSpecialFunctions.Fresnel_S_integral_piFunction
Fresnel_S_integral_pi(x)

The Fresnel function S(z) using the definition in Handbook of Mathematical Functions: Abramowitz and Stegun, where

\[ S(z) = \int_0^x \cos(\pi t^2/2) dt\]

Returns the value $S(x)$

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FewSpecialFunctions.Fresnel_C_integral_piFunction
Fresnel_C_integral_pi(x)

The Fresnel function C(z) using the definition in Handbook of Mathematical Functions: Abramowitz and Stegun, where

\[ C(z) = \int_0^x \sin(\pi t^2/2) dt\]

Returns the value $C(x)$

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FewSpecialFunctions.Fresnel_S_erfFunction
Fresnel_S_erf(x)

The Fresnel function S(z) using the definition wiki and the error function.

\[ S(z) = \sqrt{\frac{\pi}{2}} \frac{1+i}{4} \left[ \erf \left(\frac{1+i}{\sqrt{2}}z \right) - i \erf \left(\frac{1-i}{\sqrt{2}}z \right]\]

Returns the value $S(x)$

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FewSpecialFunctions.Fresnel_C_erfFunction
Fresnel_C_erf(x)

The Fresnel function C(z) using the definition wiki and the error function.

\[ C(z) = \sqrt{\frac{\pi}{2}} \frac{1-i}{4}\left[ {erf}\left(\frac{1+i}{\sqrt{2}}z \right) + i {erf}\left(\frac{1-i}{\sqrt{2}}z\right]\]

Returns the value $C(x)$

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