Built-in Mathematica Symbol

Hypergeometric1F1

Hypergeometric1F1[a, b, z]
is the Kummer confluent hypergeometric function

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For certain special arguments, Hypergeometric1F1 automatically evaluates to exact values.

Evaluate numerically:

Plot

:

Series at the origin:

Evaluate numerically:

Plot

:

Series at the origin:

Evaluate for complex arguments and parameters:

Evaluate to high precision:

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

Hypergeometric1F1 automatically evaluates to simpler functions for certain parameters:

Hypergeometric1F1 threads element-wise over list arguments and parameters:

Apply Hypergeometric1F1 to a power series:

Expand Hypergeometric1F1 in a series around infinity:

Hydrogen atom radial wave function for continuous spectrum:

Compute the energy eigenvalue from the differential equation:

Closed form for Padé approximation of Exp to any order:

Compare with explicit approximants:

Integrate may give results involving Hypergeometric1F1:

Use FunctionExpand to convert confluent hypergeometric functions: