# InverseGammaRegularized

gives the inverse of the regularized incomplete gamma function.

# Details • Mathematical function, suitable for both symbolic and numerical manipulation.
• With the regularized incomplete gamma function defined by , is the solution for in .
• InverseGammaRegularized[a,z0,s] gives the inverse of GammaRegularized[a,z0,z].
• Note that the arguments of InverseGammaRegularized are arranged differently than in InverseBetaRegularized.
• For certain special arguments, InverseGammaRegularized automatically evaluates to exact values.
• InverseGammaRegularized can be evaluated to arbitrary numerical precision.
• InverseGammaRegularized automatically threads over lists.

# Examples

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## Basic Examples(3)

Evaluate numerically:

Plot over a subset of the reals:

Series expansion at x=-1:

## Scope(20)

### Numerical Evaluation(3)

Evaluate numerically to high precision:

The precision of the output tracks the precision of the input:

Evaluate InverseGammaRegularized efficiently at high precision:

Evaluate the three-argument generalized case:

### Specific Values(3)

Values at fixed points:

Find the zero of :

Real domain of :

### Visualization(2)

Plot the inverse of the regularized gamma function for integer arguments:

Plot the real part of :

### Differentiation(3)

First derivative of the inverse of the regularized incomplete gamma function:

Higher derivatives:

First derivative of the inverse of the generalized regularized incomplete gamma function:

### Integration(2)

Indefinite integral of the inverse regularized incomplete gamma function:

Definite integral :

### Series Expansions(3)

Taylor expansion for InverseGammaRegularized around :

Plot the first three approximations for around :

Series expansion of InverseGammaRegularized at a generic point:

Series expansion of the three-parameter InverseGammaRegularized function at a generic point:

### Function Identities and Simplifications(2)

Primary definition of InverseGammaRegularized:

Function relation to its inverse:

### Other Features(2)

InverseGammaRegularized threads elementwise over lists and matrices:

## Applications(1)

Model the PDF of the gamma distribution through uniformly distributed random numbers:

Compare binned modeled distribution with exact distribution:

## Properties & Relations(2)

InverseGammaRegularized is the inverse of GammaRegularized:

Solve a transcendental equation: ## Possible Issues(2)

InverseGammaRegularized evaluates numerically only for :

In TraditionalForm, is not automatically InverseGammaRegularized:

Introduced in 1996
(3.0)