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

- Mathematical function, suitable for both symbolic and numerical manipulation.
- 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.
- Hypergeometric1F1Regularized can be evaluated to arbitrary numerical precision.
- Hypergeometric1F1Regularized automatically threads over lists.
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (32)
Numerical Evaluation (4)
Specific Values (7)
Hypergeometric1F1Regularized for symbolic a:
Find a value of x for which Hypergeometric1F1Regularized[1/2,1,x ]=0.4:
Evaluate symbolically for integer parameters:
Evaluate symbolically for half-integer parameters:
Hypergeometric1F1Regularized automatically evaluates to simpler functions for certain parameters:
Visualization (3)
Plot the Hypergeometric1F1Regularized function:
Plot Hypergeometric1F1Regularized as a function of its second parameter :
Function Properties (4)
Real domain of Hypergeometric1F1Regularized:
Complex domain of Hypergeometric1F1Regularized:
Hypergeometric1F1Regularized threads elementwise over lists:
TraditionalForm formatting:
Differentiation (3)
Integration (3)
Compute the indefinite integral using Integrate:
Series Expansions (6)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
General term in the series expansion using SeriesCoefficient:
Find the series expansion at Infinity:
Function Identities and Simplifications (2)
Use FunctionExpand to express Hypergeometric1F1Regularized through other functions:
Properties & Relations (3)
With a numeric second parameter, gives the ordinary hypergeometric function:
Hypergeometric1F1Regularized can be represented as a DifferentialRoot:
Hypergeometric1F1Regularized can be represented in terms of MeijerG:
Text
Wolfram Research (1996), Hypergeometric1F1Regularized, Wolfram Language function, https://reference.wolfram.com/language/ref/Hypergeometric1F1Regularized.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 1996. "Hypergeometric1F1Regularized." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Hypergeometric1F1Regularized.html.
APA
Wolfram Language. (1996). Hypergeometric1F1Regularized. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Hypergeometric1F1Regularized.html