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Hypergeometric1F1

Hypergeometric1F1
is the Kummer confluent hypergeometric function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The function has the series expansion .
  • For certain special arguments, Hypergeometric1F1 automatically evaluates to exact values.
Evaluate numerically:
Plot :
Series at the origin:
Evaluate numerically:
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Plot :
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Click for copyable input
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Series at the origin:
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Click for copyable input
Out[1]=
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:
TraditionalForm formatting:
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:
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