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:

Values at fixed points:

Find the zero of :

Real domain of :

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

Plot the real part of :

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:

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:

Indefinite integral of the inverse regularized incomplete gamma function:

Definite integral :

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:

Primary definition of InverseGammaRegularized:

Function relation to its inverse:

InverseGammaRegularized threads elementwise over lists and matrices:

TraditionalForm formatting: