.GNU_ScientificLibrary.Functions.specfunc

Contents

Name	Description
gamma	Gamma function
poch_ax	Pochhammer symbol (a)_x
beta_Bab	Beta function, B(a,b)
digamma	Digamma function, psi(x)
polygamma	Polygamma function, psi_n(x)
incgamma	Incomplete Gamma function, G(a,x)
erf	Error function
erfc	Complementary Error function
bessel_J0	Bessel function of the 1st kind (regular cylindrical) of order 0
bessel_Jn	Bessel function of the 1st kind (regular cylindrical) of order n
bessel_Yn	Bessel function of the 2nd kind (irregular cylindrical) of order n
bessel_In	Modified bessel function of the 1st kind (regular modified cylindrical) of order n
bessel_Kn	Modified bessel function of the 2nd kind (irregular modified cylindrical) of order n
bessel_Jnu	Bessel function of the 1st kind of order nu
bessel_Knu	Irregular modified Bessel function of order nu
bessel_zeroJnu	Zeros of Bessel function of the 1st kind of order nu
sph_bessel_jl	Spherical Bessel function of the 1st kind (regular) of order l
sph_bessel_yl	Spherical Bessel function of the 1st kind (irregular) of order l
legendre_Pl	Legendre polynomial of order l
sph_harm_Ylm	Normalized Spherical Harmonic of order l,m
hydrogen_Rnl	Normalized Hydrogen wavefunction of order n,l
fermidirac_Fmhalf	Complete Fermi-Dirac integral of order -1/2
fermidirac_Fhalf	Complete Fermi-Dirac integral of order 1/2
fermidirac_F3half	Complete Fermi-Dirac integral of order 3/2
fermidirac_Fn	Complete Fermi-Dirac integral of order n
hermite_Hn	Hermite polynomial of order n
hermite_func_psi_n	Hermite function of order n
airy_Ai	Airy Ai function
airy_Bi	Airy Bi function
airy_zeroAi	Zeros of Airy function of the 1st kind
airy_zeroBi	Zeros of Airy function of the 2nd kind
debye_D1	Debye function of order 1
debye_D2	Debye function of order 2
debye_D3	Debye function of order 3
debye_D4	Debye function of order 4
debye_D5	Debye function of order 5
debye_D6	Debye function of order 6
dilog_Li2	Dilogarithm, Li_2(x)
elliptint_K	Complete Elliptic Integral K(k)
elliptint_E	Complete Elliptic Integral E(k)
expint_En	Exponential Integral E_n(x)
expint_Ei	Exponential Integral Ei(x)
gegenpoly_Cn	Genenbauer polynomial, C_n^(a)(x)
laguerre_Ln	Laguerre functions, L_n^a(x)
lambert_W0	Lambert W_0 function
lambert_Wm1	Lambert W_-1 function
zeta	Riemann zeta function function, zeta(s)