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|[`loggamma(x)`](@ref SpecialFunctions.loggamma(::Number)) | accurate `log(gamma(x))` for large `x`|
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|[`logabsgamma(x)`](@ref SpecialFunctions.logabsgamma) | accurate `log(abs(gamma(x)))` for large `x`|
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|[`logfactorial(x)`](@ref SpecialFunctions.logfactorial) | accurate `log(factorial(x))` for large `x`; same as `loggamma(x+1)` for `x > 1`, zero otherwise |
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|[`digamma(x)`](@ref SpecialFunctions.digamma) |[digamma function](https://en.wikipedia.org/wiki/Digamma_function) (i.e. the derivative of `loggamma` at `x`) |
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|[`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) |
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|[`trigamma(x)`](@ref SpecialFunctions.trigamma) |[trigamma function](https://en.wikipedia.org/wiki/Trigamma_function) (i.e the logarithmic second derivative of `gamma` at `x`) |
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|[`polygamma(m,x)`](@ref SpecialFunctions.polygamma) |[polygamma function](https://en.wikipedia.org/wiki/Polygamma_function) (i.e the (m+1)-th derivative of the `loggamma` function at `x`) |
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|[`gamma(a,z)`](@ref SpecialFunctions.gamma(::Number,::Number)) |[upper incomplete gamma function ``\Gamma(a,z)``](https://en.wikipedia.org/wiki/Incomplete_gamma_function)|
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|[`gamma(a,z)`](@ref SpecialFunctions.gamma(::Number,::Number)) |[upper incomplete gamma function ``Γ(a,z)``](https://en.wikipedia.org/wiki/Incomplete_gamma_function)|
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|[`loggamma(a,z)`](@ref SpecialFunctions.loggamma(::Number,::Number)) | accurate `log(gamma(a,x))` for large arguments |
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|[`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)) |
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|[`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) |
@@ -34,11 +34,11 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
## Error Functions, Dawson’s and Fresnel Integrals
@@ -56,7 +56,7 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
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|[`logerfcx(x)`](@ref SpecialFunctions.logerfcx) | log of the scaled complementary error function, i.e. accurate ``\operatorname{ln}(\operatorname{erfcx}(x))`` for large negative ``x``|
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|[`erfi(x)`](@ref SpecialFunctions.erfi) | imaginary error function defined as ``-i \operatorname{erf}(ix)``|
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|[`erfinv(x)`](@ref SpecialFunctions.erfinv) | inverse function to [`erf()`](@ref SpecialFunctions.erf) |
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|[`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``|
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|[`dawson(x)`](@ref SpecialFunctions.dawson) | scaled imaginary error function, a.k.a. Dawson function, i.e. accurate ``\frac{\sqrt{π}}{2} e^{-x^2} \operatorname{erfi}(x)`` for large ``x``|
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|[`faddeeva(x)`](@ref SpecialFunctions.faddeeva) |[Faddeeva function](https://en.wikipedia.org/wiki/Faddeeva_function), equivalent to ``\operatorname{erfcx}(-ix)``|
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