gospecfunc

README

Installation

The core packages of the gospecfunc suite are written in pure Go. Installation is done using go get.

go get -u github.com/dreading/gospecfunc

Special Functions

Bessel

Bessel and related functions:

Function	Domain	Description
Ai	ℂ	Airy Ai function
Aix	ℂ	Exponentially scaled Airy Ai function
Aid	ℂ	First derivative of the Airy Ai function
Aidx	ℂ	Exponentially scaled first derivative of the Airy Ai function
Bi	ℂ	Biry Bi function
Bix	ℂ	Exponentially scaled Biry Bi function
Bid	ℂ	First derivative of the Biry Bi function
Bidx	ℂ	Exponentially scaled first derivative of the Biry Bi function
Gi	ℝ	Modified Airy Gi function
Hi	ℝ	Modified Airy Hi function
I	ℂ	Modified Bessel function of the first kind
J	ℂ	Bessel function of the first kind
K	ℂ	Modified Bessel function of the second kind
Y	ℂ	Bessel function of the second kind
H1	ℂ	Hankel fucntion of of the first kind
H2	ℂ	Hankel fucntion of of the second kind

Erf

The error function and related functions:

Function	Domain	Description
Erf	ℂ	Error function
Erfc	ℂ	Complementary error function 1 - Erf(ζ)
Erfcx	ℂ	Scaled complementary error function exp(ζ²) Erfc(ζ)
Erfi	ℂ	Imaginary error function -i erf(iζ)
Dawson	ℂ	Dawson's function. The one-sided Fourier–Laplace sine transform of the Gaussian function
Fresnel	ℂ	Cos and Sin Fresnel integrals
Voigt	ℝ	Real and imaginary Voigt functions 𝖴(x,t) and 𝖵(x,t)
Faddeyeva	ℂ	Plasma dispersion Faddeyeva function exp(-ζ²) Erfc(-iζ)

Integrals

Integrals of special functions and special integral functions:

Function	Domain	Description
Abramowitz	ℝ	Abramowitz functions of order 0,1 and 2
Clausen	ℝ	Clausen's integral
Debye	ℝ	Debye functions of order 1,2,3 and 4
Goodst	ℝ	Goodst functions
Lobach	ℝ	Lobachewsky function
Strom	ℝ	Stromgren's integral
Synch	ℝ	Synchrotron radiation function or order 1 and 2
Transport	ℝ	Transport integrals of order 2,3,4,5,6,7,8 and 9
Struve	ℝ	Struve function of order 0 and 1
StruveModified	ℝ	Modified Struve function of order 0 and 1
AtnInt	ℝ	Inverse-tangent integral
Exp3	ℝ	Exponential integral ∫ exp(-t³) dt
I0Int	ℝ	Integral of the modified Bessel function of the first kind order 0
J0Int	ℝ	Integral of the Bessel function of the first kind order 0
Y0Int	ℝ	Integral of the Bessel function of the second kind order 0
K0Int	ℝ	Integral of the modified Bessel function of the second kind order 0
AiInt	ℝ	Integral of the the Airy function Ai
BiInt	ℝ	Integral of the the Biry function Bi

Testing

 go test ./*/. 

Benchmarking

 go test -bench=. ./*/.

License

Original code is licensed under the Gonum License found in the LICENSE file. Portions of the code are subject to the additional licenses found in THIRD_PARTY_LICENSES.

Documentation

Overview

Gospecfunc is a set of packages designed to make writing numeric and scientific algorithms easy by providing accurate performant algorithms that can scale for any application.

Gonum contains libraries for bessel functions, error functions and integral of special functions.