InverseGammaRegularized

InverseGammaRegularized[a,s]

gives the inverse of the regularized incomplete gamma function.

Details

Examples

open allclose all

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 TemplateBox[{2, s}, InverseGammaRegularized]-1=0:

Real domain of TemplateBox[{a, s}, InverseGammaRegularized]:

Visualization  (2)

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

Plot the real part of TemplateBox[{a, 2, s}, InverseGammaRegularized3]:

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 int_0^1TemplateBox[{1, s}, InverseGammaRegularized]ds:

Series Expansions  (3)

Taylor expansion for InverseGammaRegularized around :

Plot the first three approximations for TemplateBox[{1, s}, InverseGammaRegularized] 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:

TraditionalForm formatting:

Generalizations & Extensions  (1)

InverseGammaRegularized threads element-wise over lists:

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:

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.

BibTeX

@misc{reference.wolfram_2020_inversegammaregularized, author="Wolfram Research", title="{InverseGammaRegularized}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InverseGammaRegularized.html}", note=[Accessed: 15-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_inversegammaregularized, organization={Wolfram Research}, title={InverseGammaRegularized}, year={1996}, url={https://reference.wolfram.com/language/ref/InverseGammaRegularized.html}, note=[Accessed: 15-January-2021 ]}

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