Add Inverse of Incomplete Gamma Function P(a,x) and Q(a,x) (#164)

Author: Sumegh-git

docs/src/index.md

@@ -19,7 +19,8 @@ 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)) |
+| [`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)) |
+| [`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`)  |
 | [`eta(x)`](@ref SpecialFunctions.eta)                         | [Dirichlet eta function](https://en.wikipedia.org/wiki/Dirichlet_eta_function) at `x`                                                                           |

docs/src/special.md

@@ -50,6 +50,7 @@ SpecialFunctions.eta
 SpecialFunctions.zeta
 SpecialFunctions.gamma
 SpecialFunctions.gamma_inc
+SpecialFunctions.gamma_inc_inv
 SpecialFunctions.loggamma
 SpecialFunctions.logabsgamma
 SpecialFunctions.logfactorial

src/SpecialFunctions.jl

@@ -48,6 +48,7 @@ export
     polygamma,
     trigamma,
     gamma_inc,
+    gamma_inc_inv,
     hankelh1,
     hankelh1x,
     hankelh2,