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updated deprecated makedocs call: format; clean build dir; aligned code #167

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Aug 13, 2019
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updated deprecated makedocs call: format; clean build dir; aligned code #167

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8d3b530
updated deprecated makedocs call: format; clean build dir; aligned code
PaulXiCao Jun 17, 2019
7c323fa
split up of documentation. WIP
PaulXiCao Jun 17, 2019
a294323
new documentation layout: erf, erfc
PaulXiCao Jun 20, 2019
5a7eeab
added erfi; new layout
PaulXiCao Jun 20, 2019
ad5bc54
Merge remote-tracking branch 'upstream/master' into doc-makefile
PaulXiCao Aug 9, 2019
5de1111
error functions
PaulXiCao Aug 9, 2019
460d79f
Merge remote-tracking branch 'upstream/master' into doc-makefile
PaulXiCao Aug 10, 2019
061ac6b
ellipk: added documentation
PaulXiCao Aug 10, 2019
ac0fb62
ellipk: aligned source code. renamed variables.
PaulXiCao Aug 10, 2019
b9880be
ellipe: added documentation
PaulXiCao Aug 10, 2019
b95fcdf
ellipe: aligned source code. renamed variables.
PaulXiCao Aug 10, 2019
ff10cdb
ellipk: added documentation
PaulXiCao Aug 10, 2019
387bdbd
ellipe: added documentation
PaulXiCao Aug 11, 2019
c5a0133
ellip: added tests -> increased code coverage
PaulXiCao Aug 11, 2019
9246b92
ellip: subdivided tests
PaulXiCao Aug 11, 2019
2a1630c
ellipk: added test
PaulXiCao Aug 11, 2019
d44bb18
erf: added tests for each type, regrouped tests
PaulXiCao Aug 11, 2019
b7eb56b
sincosint: added documentation
PaulXiCao Aug 12, 2019
8e07581
sincosint: updated tests: added complex args
PaulXiCao Aug 12, 2019
0843aac
sincosint: aligned source code.
PaulXiCao Aug 12, 2019
b9cd41a
generally grouped functions
PaulXiCao Aug 12, 2019
7c5c287
captitalization of headings
PaulXiCao Aug 13, 2019
8ec171b
gamma: documentation
PaulXiCao Aug 13, 2019
83c1ee8
gamma: regrouped source code. bigfloat doc.
PaulXiCao Aug 13, 2019
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19 changes: 9 additions & 10 deletions docs/make.jl
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Original file line number Diff line number Diff line change
@@ -1,18 +1,17 @@
using SpecialFunctions, Documenter

makedocs(
modules = [SpecialFunctions],
clean = false,
format = :html,
sitename = "SpecialFunctions.jl",
authors = "Jeff Bezanson, Stefan Karpinski, Viral B. Shah, et al.",
pages = [
"Home" => "index.md",
"Functions" => "special.md",
modules = [SpecialFunctions],
sitename = "SpecialFunctions.jl",
authors = "Jeff Bezanson, Stefan Karpinski, Viral B. Shah, et al.",
pages = [
"Home" => "index.md",
"Overview" => "functions_overview.md",
"List" => "functions_list.md",
],
)

deploydocs(
repo = "github.com/JuliaMath/SpecialFunctions.jl.git",
target = "build",
repo = "github.com/JuliaMath/SpecialFunctions.jl.git",
target = "build",
)
0 docs/src/special.md → docs/src/functions_list.md
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80 changes: 80 additions & 0 deletions docs/src/functions_overview.md
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@@ -0,0 +1,80 @@
# Functions
Here the *Special Functions* are listed according to the structure of [NIST Digital Library of Mathematical Functions](https://dlmf.nist.gov/).

## Error Functions, Dawson’s and Fresnel Integrals

| Function | Description |
|:-------- |:----------- |
| [`erf(x)`](@ref SpecialFunctions.erf) | [error function](https://en.wikipedia.org/wiki/Error_function) at ``x`` |
| [`erfc(x)`](@ref SpecialFunctions.erfc) | complementary error function, i.e. the accurate version of ``1-\operatorname{erf}(x)`` for large ``x`` |
| [`erfcinv(x)`](@ref SpecialFunctions.erfcinv) | inverse function to [`erfc()`](@ref SpecialFunctions.erfc) |
| [`erfcx(x)`](@ref SpecialFunctions.erfcx) | scaled complementary error function, i.e. accurate ``e^{x^2} \operatorname{erfc}(x)`` for large ``x`` |
| [`erfi(x)`](@ref SpecialFunctions.erfi) | imaginary error function defined as ``-i \operatorname{erf}(ix)`` |
| [`erfinv(x)`](@ref SpecialFunctions.erfinv) | inverse function to [`erf()`](@ref SpecialFunctions.erf) |
| [`dawson(x)`](@ref SpecialFunctions.dawson) | scaled imaginary error function, a.k.a. Dawson function, i.e. accurate ``\frac{\sqrt{\pi}}{2} e^{-x^2} \operatorname{erfi}(x)`` for large ``x`` |


## Elliptic Integrals

| Function | Description |
|:-------- |:----------- |
| [`ellipk(m)`](@ref SpecialFunctions.ellipk) | [complete elliptic integral of 1st kind](https://en.wikipedia.org/wiki/Elliptic_integral#Notational_variants) ``K(m)`` |
| [`ellipe(m)`](@ref SpecialFunctions.ellipe) | [complete elliptic integral of 2nd kind](https://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_second_kind) ``E(m)`` |

## Trigonometric Integrals
| Function | Description |
|:-------- |:----------- |
| [`sinint(x)`](@ref SpecialFunctions.sinint) | [sine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Sine_integral) ``Si(x)`` |
| [`cosint(x)`](@ref SpecialFunctions.cosint) | [cosine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Cosine_integral) ``Ci(x)`` |

## Airy, Bessel and Hankel Functions
| Function | Description |
|:-------- |:----------- |
| [`airyai(z)`](@ref SpecialFunctions.airyai) | [Airy Ai function](https://en.wikipedia.org/wiki/Airy_function) at `z` |
| [`airyaiprime(z)`](@ref SpecialFunctions.airyaiprime) | derivative of the Airy Ai function at `z` |
| [`airybi(z)`](@ref SpecialFunctions.airybi) | [Airy Bi function](https://en.wikipedia.org/wiki/Airy_function) at `z` |
| [`airybiprime(z)`](@ref SpecialFunctions.airybiprime) | derivative of the Airy Bi function at `z` |
| [`airyaix(z)`](@ref SpecialFunctions.airyaix), [`airyaiprimex(z)`](@ref SpecialFunctions.airyaiprimex), [`airybix(z)`](@ref SpecialFunctions.airybix), [`airybiprimex(z)`](@ref SpecialFunctions.airybiprimex) | scaled Airy Ai function and `k`th derivatives at `z` |
| [`besselj(nu,z)`](@ref SpecialFunctions.besselj) | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind of order `nu` at `z` |
| [`besselj0(z)`](@ref SpecialFunctions.besselj0) | `besselj(0,z)` |
| [`besselj1(z)`](@ref SpecialFunctions.besselj1) | `besselj(1,z)` |
| [`besseljx(nu,z)`](@ref SpecialFunctions.besseljx) | scaled Bessel function of the first kind of order `nu` at `z` |
| [`bessely(nu,z)`](@ref SpecialFunctions.bessely) | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind of order `nu` at `z` |
| [`bessely0(z)`](@ref SpecialFunctions.bessely0) | `bessely(0,z)` |
| [`bessely1(z)`](@ref SpecialFunctions.bessely1) | `bessely(1,z)` |
| [`besselyx(nu,z)`](@ref SpecialFunctions.besselyx) | scaled Bessel function of the second kind of order `nu` at `z` |
| [`besselh(nu,k,z)`](@ref SpecialFunctions.besselh) | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the third kind (a.k.a. Hankel function) of order `nu` at `z`; `k` must be either `1` or `2` |
| [`hankelh1(nu,z)`](@ref SpecialFunctions.hankelh1) | `besselh(nu, 1, z)` |
| [`hankelh1x(nu,z)`](@ref SpecialFunctions.hankelh1x) | scaled `besselh(nu, 1, z)` |
| [`hankelh2(nu,z)`](@ref SpecialFunctions.hankelh2) | `besselh(nu, 2, z)` |
| [`hankelh2x(nu,z)`](@ref SpecialFunctions.hankelh2x) | scaled `besselh(nu, 2, z)` |
| [`besseli(nu,z)`](@ref SpecialFunctions.besseli) | modified [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind of order `nu` at `z` |
| [`besselix(nu,z)`](@ref SpecialFunctions.besselix) | scaled modified Bessel function of the first kind of order `nu` at `z` |
| [`besselk(nu,z)`](@ref SpecialFunctions.besselk) | modified [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind of order `nu` at `z` |
| [`besselkx(nu,z)`](@ref SpecialFunctions.besselkx) | scaled modified Bessel function of the second kind of order `nu` at `z` |

## Gamma and related functions
| Function | Description |
|:-------- |:----------- |
| [`gamma(z)`](@ref SpecialFunctions.gamma) | [gamma function](https://en.wikipedia.org/wiki/Gamma_function) ``\Gamma(z)`` |
| [`digamma(x)`](@ref SpecialFunctions.digamma) | [digamma function](https://en.wikipedia.org/wiki/Digamma_function) (i.e. the derivative of `lgamma` at `x`) |
| [`invdigamma(x)`](@ref SpecialFunctions.invdigamma) | [invdigamma function](http://bariskurt.com/calculating-the-inverse-of-digamma-function/) (i.e. inverse of `digamma` function at `x` using fixed-point iteration algorithm) |
| [`trigamma(x)`](@ref SpecialFunctions.trigamma) | [trigamma function](https://en.wikipedia.org/wiki/Trigamma_function) (i.e the logarithmic second derivative of `gamma` at `x`) |
| [`polygamma(m,x)`](@ref SpecialFunctions.polygamma) | [polygamma function](https://en.wikipedia.org/wiki/Polygamma_function) (i.e the (m+1)-th derivative of the `lgamma` function at `x`) |
| [`gamma_inc(a,x,IND)`](@ref SpecialFunctions.gamma_inc) | [incomplete gamma function ratio P(a,x) and Q(a,x)](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates P(a,x) and Q(a,x)for accuracy specified by IND and returns tuple (p,q)) |
| [`beta_inc(a,b,x,y)`](@ref SpecialFunctions.beta_inc) | [incomplete beta function ratio Ix(a,b) and Iy(a,b)](https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function) (i.e evaluates Ix(a,b) and Iy(a,b) and returns tuple (p,q)) |
| [`gamma_inc_inv(a,p,q)`](@ref SpecialFunctions.gamma_inc_inv) | [inverse of incomplete gamma function ratio P(a,x) and Q(a,x)](https://en.wikipedia.org/wiki/Incomplete_gamma_function) (i.e evaluates x given P(a,x)=p and Q(a,x)=q |
| [`loggamma(x)`](@ref SpecialFunctions.loggamma) | accurate `log(gamma(x))` for large `x` |
| [`logabsgamma(x)`](@ref SpecialFunctions.logabsgamma) | accurate `log(abs(gamma(x)))` for large `x` |
| [`lgamma(x)`](@ref SpecialFunctions.lgamma) | accurate `log(gamma(x))` for large `x` |
| [`logfactorial(x)`](@ref SpecialFunctions.logfactorial) | accurate `log(factorial(x))` for large `x`; same as `lgamma(x+1)` for `x > 1`, zero otherwise |
| [`beta(x,y)`](@ref SpecialFunctions.beta) | [beta function](https://en.wikipedia.org/wiki/Beta_function) at `x,y` |
| [`logbeta(x,y)`](@ref SpecialFunctions.logbeta) | accurate `log(beta(x,y))` for large `x` or `y` |
| [`logabsbeta(x,y)`](@ref SpecialFunctions.logabsbeta) | accurate `log(abs(beta(x,y)))` for large `x` or `y` |
| [`logabsbinomial(x,y)`](@ref SpecialFunctions.logabsbinomial) | accurate `log(abs(beta(x,y)))` for large `x` or `y` |

## Riemann Zeta and related functions
| Function | Description |
|:-------- |:----------- |
| [`eta(x)`](@ref SpecialFunctions.eta) | [Dirichlet eta function](https://en.wikipedia.org/wiki/Dirichlet_eta_function) at `x` |
| [`zeta(x)`](@ref SpecialFunctions.zeta) | [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) at `x` |
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