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HypergeometricU

HypergeometricU
is the confluent hypergeometric function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The function has the integral representation .
  • HypergeometricU has a branch cut discontinuity in the complex plane running from to .
  • For certain special arguments, HypergeometricU automatically evaluates to exact values.
Evaluate numerically:
Plot :
Series expansion at the origin:
Evaluate numerically:
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Plot :
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Series expansion at the origin:
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Click for copyable input
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Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
HypergeometricU threads element-wise over lists:
HypergeometricU automatically evaluates to simpler functions for certain parameters:
TraditionalForm formatting:
Expand HypergeometricU in series around infinity:
Solve the confluent hypergeometric differential equation:
Borel summation of divergent series of gives HypergeometricU:
Use FunctionExpand to expand HypergeometricU into simpler functions:
Integrate may give results involving HypergeometricU:
The default setting of $MaxExtraPrecision can be insufficient to obtain requested precision:
A larger setting for $MaxExtraPrecision may be needed:
Visualize the confluency relation :
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