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Built-in Mathematica Symbol

Hypergeometric1F1Regularized

Hypergeometric1F1Regularized[a, b, z]
is the regularized confluent hypergeometric function

Hypergeometric1F1Regularized[a, b, z] is finite for all finite values of a, b and z.

For certain special arguments, Hypergeometric1F1Regularized automatically evaluates to exact values.

Evaluate numerically:

Series expansion at the origin:

Evaluate numerically:

Series expansion at the origin:

Evaluate for complex arguments and parameters:

Evaluate to high precision:

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

Evaluate to simpler functions for certain parameters:

Hypergeometric1F1Regularized threads element-wise over lists:

Series expansion at infinity:

With a numeric second parameter, gives the ordinary hypergeometric function:

Visualize the confluence relation