# InverseGammaRegularized

gives the inverse of the regularized incomplete gamma function.

# Examples

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## Basic Examples(3)

Evaluate numerically:

Plot over a subset of the reals:

Series expansion at x=-1:

## Scope(30)

### Numerical Evaluation(5)

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:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix InverseGammaRegularized function using MatrixFunction:

### 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 :

### Function Properties(8)

Real domain of InverseGammaRegularized:

Its complex domain is the same:

The range of InverseGammaRegularized is the non-negative reals:

InverseGammaRegularized is not an analytic function:

It has both singularities and discontinuities:

For a fixed value of , is nonincreasing on its domain:

For a fixed value of , is an injective function of :

InverseGammaRegularized is not surjective:

InverseGammaRegularized is non-negative on its domain:

InverseGammaRegularized is neither convex nor concave:

### 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(2)

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

Compare binned modeled distribution with exact distribution:

Quartiles for a derived distribution:

Data 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:

Wolfram Research (1996), InverseGammaRegularized, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseGammaRegularized.html.

#### Text

Wolfram Research (1996), InverseGammaRegularized, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseGammaRegularized.html.

#### CMS

Wolfram Language. 1996. "InverseGammaRegularized." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseGammaRegularized.html.

#### APA

Wolfram Language. (1996). InverseGammaRegularized. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseGammaRegularized.html

#### BibTeX

@misc{reference.wolfram_2024_inversegammaregularized, author="Wolfram Research", title="{InverseGammaRegularized}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InverseGammaRegularized.html}", note=[Accessed: 16-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversegammaregularized, organization={Wolfram Research}, title={InverseGammaRegularized}, year={1996}, url={https://reference.wolfram.com/language/ref/InverseGammaRegularized.html}, note=[Accessed: 16-September-2024 ]}