InverseGammaRegularized

InverseGammaRegularized[a,s]

gives the inverse of the regularized incomplete gamma function.

Details

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 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:

Introduced in 1996
 (3.0)