Bessel functions.
This module provides implementation for the Bessel functions and related operations.
Required header:
Variables | |
constexpr callable_airy_ | eve::airy = {} |
Computes the airy functions values \( Ai(x)\) and \( Bi(x)\). More... | |
constexpr callable_airy_ai_ | eve::airy_ai = {} |
Computes the airy function \( Ai(x)\). More... | |
constexpr callable_airy_bi_ | eve::airy_bi = {} |
Computes the airy function \( Bi(x)\). More... | |
constexpr callable_cyl_bessel_i0_ | eve::cyl_bessel_i0 = {} |
Computes the modified Bessel function of the first kind, \( I_0(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}\,\mathrm{d}\tau\). More... | |
constexpr callable_cyl_bessel_i1_ | eve::cyl_bessel_i1 = {} |
Computes the modified Bessel function of the first kind, \( I_1(x)=\frac1{\pi}\int_{0}^{\pi}e^{x\cos\tau}\cos\tau\,\mathrm{d}\tau\). More... | |
constexpr callable_cyl_bessel_in_ | eve::cyl_bessel_in = {} |
Computes the modified Bessel functions of the first kind, \( I_{n}(x)=\left(\frac12z\right)^n\sum_{k=0}^{\infty}{\frac{(x^2/4)^k}
{k!\,\Gamma (k+n +1)}}\). More... | |
constexpr callable_cyl_bessel_j0_ | eve::cyl_bessel_j0 = {} |
Computes the Bessel function of the first kind, \( J_0(x)=\frac1{\pi }\int _{0}^{\pi}\cos(x\sin \tau)
\,\mathrm {d} \tau \). More... | |
constexpr callable_cyl_bessel_j1_ | eve::cyl_bessel_j1 = {} |
Computes the Bessel function of the first kind, \( J_1(x)=\frac1{\pi }\int _{0}^{\pi}\cos(\tau-x\sin \tau )\,\mathrm {d} \tau \). More... | |
constexpr callable_cyl_bessel_jn_ | eve::cyl_bessel_jn = {} |
Computes the Bessel functions of the first kind, \( J_{n}(x)=\sum_{p=0}^{\infty}{\frac{(-1)^p}{p!\,\Gamma (p+n +1)}}
{\left({x \over 2}\right)}^{2p+n }\). More... | |
constexpr callable_cyl_bessel_k0_ | eve::cyl_bessel_k0 = {} |
Computes the modified Bessel function of the second kind, \( K_0(x)=\int_{0}^{\infty}\frac{\cos(x\tau)}
{\sqrt{\tau^2+1}}\,\mathrm{d}\tau\). More... | |
constexpr callable_cyl_bessel_k1_ | eve::cyl_bessel_k1 = {} |
Computes the modified Bessel function of the second kind, \( K_1(x)=\int_{0}^{\infty} e^{-x \cosh \tau} \cosh \tau\,\mathrm{d}\tau\). More... | |
constexpr callable_cyl_bessel_kn_ | eve::cyl_bessel_kn = {} |
Computes the modified Bessel function of the second kind, \( K_n(x)=\frac{\Gamma(n+1/2)(2x)^n}{\sqrt\pi} \int_{0}^{\infty}\frac{\cos\tau}
{(\tau^2+x^2)^{n+1/2}}\,\mathrm{d}\tau\). More... | |
constexpr callable_cyl_bessel_y0_ | eve::cyl_bessel_y0 = {} |
Computes the Bessel function of the second kind, \( Y_0(x)=\frac2{\pi}\int_{1}^{\infty}\frac{\cos x\tau}
{\sqrt{\tau^2-1}}\,\mathrm {d} \tau\). More... | |
constexpr callable_cyl_bessel_y1_ | eve::cyl_bessel_y1 = {} |
Computes the Bessel function of the second kind, \( Y_1(x)=\frac2{\pi}\int_{1}^{\infty}\frac{\cos x\tau}
{(\tau^2-1)^{3/2}}\,\mathrm{d}\tau\). More... | |
constexpr callable_cyl_bessel_yn_ | eve::cyl_bessel_yn = {} |
Computes the Bessel functions of the second kind, \( Y_{n}(x)=\frac{2(z/2)^{-n}}{\sqrt\pi\, \Gamma(1/2-n)}\int _{1}^{\infty}\frac{\cos x\tau}
{(\tau^2-1)^{n+1/2}}\,\mathrm {d} \tau \). More... | |
constexpr callable_sph_bessel_j0_ | eve::sph_bessel_j0 = {} |
Computes the spherical Bessel function of the first kind, \( j_{0}(x)= \sqrt{\frac\pi{2x}}J_{1/2}(x) \). More... | |
constexpr callable_sph_bessel_j1_ | eve::sph_bessel_j1 = {} |
Computes the spherical Bessel function of the first kind, \( j_{1}(x)= \sqrt{\frac\pi{2x}}J_{3/2}(x) \). More... | |
constexpr callable_sph_bessel_jn_ | eve::sph_bessel_jn = {} |
Computes the spherical Bessel functions of the first kind, \( j_{n}(x)= \sqrt{\frac\pi{2x}}J_{n+1/2}(x)\). More... | |
constexpr callable_sph_bessel_y0_ | eve::sph_bessel_y0 = {} |
Computes the spherical Bessel function of the second kind, \( y_{0}(x)= \sqrt{\frac\pi{2x}}Y_{1/2}(x) \). More... | |
constexpr callable_sph_bessel_y1_ | eve::sph_bessel_y1 = {} |
Computes the spherical Bessel function of the second kind, \( y_{1}(x)= \sqrt{\frac\pi{2x}}Y_{3/2}(x) \). More... | |
constexpr callable_sph_bessel_yn_ | eve::sph_bessel_yn = {} |
Computes the the spherical Bessel functions of the second kind, \( y_{n}(x)= \sqrt{\frac\pi{2x}}Y_{n+1/2}(x)\). More... | |