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Add Incomplete Beta Function ratios Ix(a,b) and Iy(a,b) #165

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Jun 10, 2019
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1 change: 1 addition & 0 deletions docs/src/index.md
Original file line number Diff line number Diff line change
Expand Up @@ -20,6 +20,7 @@ libraries.
| [`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 |
| [`ellipk(x)`](@ref SpecialFunctions.ellipk) | [complete elliptic integral of 1st kind](https://en.wikipedia.org/wiki/Elliptic_integral) (i.e evaluates complete elliptic integral of 1st kind at `x`) |
| [`ellipe(x)`](@ref SpecialFunctions.ellipe) | [complete elliptic integral of 2nd kind](https://en.wikipedia.org/wiki/Elliptic_integral) (i.e evaluates complete elliptic integral of 2nd kind at `x`) |
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1 change: 1 addition & 0 deletions docs/src/special.md
Original file line number Diff line number Diff line change
Expand Up @@ -51,6 +51,7 @@ SpecialFunctions.zeta
SpecialFunctions.gamma
SpecialFunctions.gamma_inc
SpecialFunctions.gamma_inc_inv
SpecialFunctions.beta_inc
SpecialFunctions.loggamma
SpecialFunctions.logabsgamma
SpecialFunctions.logfactorial
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2 changes: 2 additions & 0 deletions src/SpecialFunctions.jl
Original file line number Diff line number Diff line change
Expand Up @@ -48,6 +48,7 @@ export
polygamma,
trigamma,
gamma_inc,
beta_inc,
gamma_inc_inv,
hankelh1,
hankelh1x,
Expand All @@ -64,6 +65,7 @@ include("ellip.jl")
include("sincosint.jl")
include("gamma.jl")
include("gamma_inc.jl")
include("beta_inc.jl")
include("deprecated.jl")

for f in (:digamma, :erf, :erfc, :erfcinv, :erfcx, :erfi, :erfinv,
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