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Fix documentation references
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docs/src/index.md

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| Function | Description |
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|:------------------------------------------------------------- |:--------------------------------------------------------------------------------------------------------------------------------------------------------------- |
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| [`erf(x)`](@ref) | [error function](https://en.wikipedia.org/wiki/Error_function) at `x` |
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| [`erfc(x)`](@ref) | complementary error function, i.e. the accurate version of `1-erf(x)` for large `x` |
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| [`erfinv(x)`](@ref) | inverse function to [`erf()`](@ref) |
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| `erfcinv(x)` | inverse function to [`erfc()`](@ref) |
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| [`erfi(x)`](@ref) | imaginary error function defined as `-im * erf(x * im)`, where [`im`](@ref) is the imaginary unit |
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| [`erfcx(x)`](@ref) | scaled complementary error function, i.e. accurate `exp(x^2) * erfc(x)` for large `x` |
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| [`dawson(x)`](@ref) | scaled imaginary error function, a.k.a. Dawson function, i.e. accurate `exp(-x^2) * erfi(x) * sqrt(pi) / 2` for large `x` |
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| [`digamma(x)`](@ref) | [digamma function](https://en.wikipedia.org/wiki/Digamma_function) (i.e. the derivative of [`lgamma()`](@ref)) at `x` |
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| [`eta(x)`](@ref) | [Dirichlet eta function](https://en.wikipedia.org/wiki/Dirichlet_eta_function) at `x` |
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| [`zeta(x)`](@ref) | [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) at `x` |
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| [`airyai(z)`](@ref) | [Airy Ai function](https://en.wikipedia.org/wiki/Airy_function) at `z` |
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| [`airyaiprime(z)`](@ref) | derivative of the Airy Ai function at `z` |
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| [`airybi(z)`](@ref) | [Airy Bi function](https://en.wikipedia.org/wiki/Airy_function) at `z` |
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| [`airybiprime(z)`](@ref) | derivative of the Airy Bi function at `z` |
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| [`airyaix(z)`](@ref), [`airyaiprimex(z)`](@ref), [`airybix(z)`](@ref), [`airybiprimex(z)`](@ref) | scaled Airy AI function and `k` th derivatives at `z` |
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| [`besselj(nu,z)`](@ref) | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind of order `nu` at `z` |
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| [`besselj0(z)`](@ref) | `besselj(0,z)` |
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| [`besselj1(z)`](@ref) | `besselj(1,z)` |
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| [`besseljx(nu,z)`](@ref) | scaled Bessel function of the first kind of order `nu` at `z` |
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| [`bessely(nu,z)`](@ref) | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind of order `nu` at `z` |
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| [`bessely0(z)`](@ref) | `bessely(0,z)` |
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| [`bessely1(z)`](@ref) | `bessely(1,z)` |
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| [`besselyx(nu,z)`](@ref) | scaled Bessel function of the second kind of order `nu` at `z` |
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| [`besselh(nu,k,z)`](@ref) | [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` |
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| [`hankelh1(nu,z)`](@ref) | `besselh(nu, 1, z)` |
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| [`hankelh1x(nu,z)`](@ref) | scaled `besselh(nu, 1, z)` |
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| [`hankelh2(nu,z)`](@ref) | `besselh(nu, 2, z)` |
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| [`hankelh2x(nu,z)`](@ref) | scaled `besselh(nu, 2, z)` |
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| [`besseli(nu,z)`](@ref) | modified [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind of order `nu` at `z` |
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| [`besselix(nu,z)`](@ref) | scaled modified Bessel function of the first kind of order `nu` at `z` |
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| [`besselk(nu,z)`](@ref) | modified [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind of order `nu` at `z` |
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| [`besselkx(nu,z)`](@ref) | scaled modified Bessel function of the second kind of order `nu` at `z` |
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| [`erf(x)`](@ref SpecialFunctions.erf) | [error function](https://en.wikipedia.org/wiki/Error_function) at `x` |
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| [`erfc(x)`](@ref SpecialFunctions.erfc) | complementary error function, i.e. the accurate version of `1-erf(x)` for large `x` |
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| [`erfinv(x)`](@ref SpecialFunctions.erfinv) | inverse function to [`erf()`](@ref SpecialFunctions.erf) |
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| [`erfcinv(x)`](@ref SpecialFunctions.erfcinv) | inverse function to [`erfc()`](@ref SpecialFunctions.erfc) |
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| [`erfi(x)`](@ref SpecialFunctions.erfi) | imaginary error function defined as `-im * erf(x * im)`, where `im` is the imaginary unit |
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| [`erfcx(x)`](@ref SpecialFunctions.erfcx) | scaled complementary error function, i.e. accurate `exp(x^2) * erfc(x)` for large `x` |
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| [`dawson(x)`](@ref SpecialFunctions.dawson) | scaled imaginary error function, a.k.a. Dawson function, i.e. accurate `exp(-x^2) * erfi(x) * sqrt(pi) / 2` for large `x` |
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| [`digamma(x)`](@ref SpecialFunctions.digamma) | [digamma function](https://en.wikipedia.org/wiki/Digamma_function) (i.e. the derivative of `lgamma` at `x`) |
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| [`eta(x)`](@ref SpecialFunctions.eta) | [Dirichlet eta function](https://en.wikipedia.org/wiki/Dirichlet_eta_function) at `x` |
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| [`zeta(x)`](@ref SpecialFunctions.zeta) | [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) at `x` |
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| [`airyai(z)`](@ref SpecialFunctions.airyai) | [Airy Ai function](https://en.wikipedia.org/wiki/Airy_function) at `z` |
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| [`airyaiprime(z)`](@ref SpecialFunctions.airyaiprime) | derivative of the Airy Ai function at `z` |
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| [`airybi(z)`](@ref SpecialFunctions.airybi) | [Airy Bi function](https://en.wikipedia.org/wiki/Airy_function) at `z` |
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| [`airybiprime(z)`](@ref SpecialFunctions.airybiprime) | derivative of the Airy Bi function at `z` |
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| [`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` |
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| [`besselj(nu,z)`](@ref SpecialFunctions.besselj) | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind of order `nu` at `z` |
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| [`besselj0(z)`](@ref SpecialFunctions.besselj0) | `besselj(0,z)` |
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| [`besselj1(z)`](@ref SpecialFunctions.besselj1) | `besselj(1,z)` |
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| [`besseljx(nu,z)`](@ref SpecialFunctions.besseljx) | scaled Bessel function of the first kind of order `nu` at `z` |
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| [`bessely(nu,z)`](@ref SpecialFunctions.bessely) | [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind of order `nu` at `z` |
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| [`bessely0(z)`](@ref SpecialFunctions.bessely0) | `bessely(0,z)` |
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| [`bessely1(z)`](@ref SpecialFunctions.bessely1) | `bessely(1,z)` |
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| [`besselyx(nu,z)`](@ref SpecialFunctions.besselyx) | scaled Bessel function of the second kind of order `nu` at `z` |
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| [`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` |
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| [`hankelh1(nu,z)`](@ref SpecialFunctions.hankelh1) | `besselh(nu, 1, z)` |
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| [`hankelh1x(nu,z)`](@ref SpecialFunctions.hankelh1x) | scaled `besselh(nu, 1, z)` |
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| [`hankelh2(nu,z)`](@ref SpecialFunctions.hankelh2) | `besselh(nu, 2, z)` |
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| [`hankelh2x(nu,z)`](@ref SpecialFunctions.hankelh2x) | scaled `besselh(nu, 2, z)` |
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| [`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` |
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| [`besselix(nu,z)`](@ref SpecialFunctions.besselix) | scaled modified Bessel function of the first kind of order `nu` at `z` |
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| [`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` |
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| [`besselkx(nu,z)`](@ref SpecialFunctions.besselkx) | scaled modified Bessel function of the second kind of order `nu` at `z` |
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## Installation
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docs/src/special.md

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# Functions
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```@meta
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CurrentModule = SpecialFunctions
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```
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```@docs
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SpecialFunctions.erf
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SpecialFunctions.erfc
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SpecialFunctions.besselk
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SpecialFunctions.besselkx
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SpecialFunctions.eta
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SpecialFunctions.zeta(::Complex)
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SpecialFunctions.zeta(::Any, ::Any)
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SpecialFunctions.zeta
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```

src/bessel.jl

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airyaix(x)
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Scaled Airy function of the first kind ``\\operatorname{Ai}(x) e^{\\frac{2}{3} x
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\\sqrt{x}}``. Throws [`DomainError`](@ref) for negative `Real` arguments.
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\\sqrt{x}}``. Throws `DomainError` for negative `Real` arguments.
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"""
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function airyaix end
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airyaix(z::Complex128) = _airy(z, Int32(0), Int32(2))
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airyaiprimex(x)
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Scaled derivative of the Airy function of the first kind ``\\operatorname{Ai}'(x)
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e^{\\frac{2}{3} x \\sqrt{x}}``. Throws [`DomainError`](@ref) for negative `Real` arguments.
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e^{\\frac{2}{3} x \\sqrt{x}}``. Throws `DomainError` for negative `Real` arguments.
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"""
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function airyaiprimex end
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airyaiprimex(z::Complex128) = _airy(z, Int32(1), Int32(2))

src/gamma.jl

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"""
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digamma(x)
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Compute the digamma function of `x` (the logarithmic derivative of [`gamma(x)`](@ref)).
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Compute the digamma function of `x` (the logarithmic derivative of `gamma(x)`).
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"""
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function digamma(z::Union{Float64,Complex{Float64}})
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# Based on eq. (12), without looking at the accompanying source
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"""
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trigamma(x)
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Compute the trigamma function of `x` (the logarithmic second derivative of [`gamma(x)`](@ref)).
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Compute the trigamma function of `x` (the logarithmic second derivative of `gamma(x)`).
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"""
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function trigamma(z::Union{Float64,Complex{Float64}})
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# via the derivative of the Kölbig digamma formulation
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polygamma(m, x)
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Compute the polygamma function of order `m` of argument `x` (the `(m+1)th` derivative of the
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logarithm of [`gamma(x)`](@ref))
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logarithm of `gamma(x)`)
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"""
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function polygamma(m::Integer, z::Union{Float64,Complex{Float64}})
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m == 0 && return digamma(z)

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