Added incomplete gamma function ratios P(a,x) and Q(a,x) (#146)

Author: Sumegh-git

docs/src/index.md

@@ -19,6 +19,7 @@ libraries.
 | [`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_p)  | [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)) |
 | [`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`)  |
 | [`eta(x)`](@ref SpecialFunctions.eta)                         | [Dirichlet eta function](https://en.wikipedia.org/wiki/Dirichlet_eta_function) at `x`                                                                           |

docs/src/special.md

@@ -49,6 +49,7 @@ SpecialFunctions.ellipe
 SpecialFunctions.eta
 SpecialFunctions.zeta
 SpecialFunctions.gamma
+SpecialFunctions.gamma_inc
 SpecialFunctions.loggamma
 SpecialFunctions.logabsgamma
 SpecialFunctions.logfactorial

src/SpecialFunctions.jl

@@ -10,7 +10,6 @@ let depsjl_path = joinpath(@__DIR__, "..", "deps", "deps.jl")
 end
 
 __init__() = check_deps()
-
 export
     airyai,
     airyaiprime,
@@ -48,6 +47,7 @@ export
     invdigamma,
     polygamma,
     trigamma,
+    gamma_inc,
     hankelh1,
     hankelh1x,
     hankelh2,
@@ -62,6 +62,7 @@ include("erf.jl")
 include("ellip.jl")
 include("sincosint.jl")
 include("gamma.jl")
+include("gamma_inc.jl")
 include("deprecated.jl")
 
 for f in (:digamma, :erf, :erfc, :erfcinv, :erfcx, :erfi, :erfinv,