is the regularized confluent hypergeometric function .
- 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.
- Hypergeometric1F1Regularized can be used with Interval and CenteredInterval objects. »
Examplesopen allclose all
Basic 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:
Numerical Evaluation (5)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
Hypergeometric1F1Regularized can be used with Interval and CenteredInterval objects:
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:
Plot the Hypergeometric1F1Regularized function:
Plot Hypergeometric1F1Regularized as a function of its second parameter :
Function Properties (10)
Hypergeometric1F1Regularized is defined for all real and complex values:
Hypergeometric1F1Regularized threads elementwise over lists:
Hypergeometric1F1Regularized is neither non-decreasing nor non-increasing except for special values:
Hypergeometric1F1Regularized is non-negative for specific values:
is neither non-negative nor non-positive:
has no singularities or discontinuities:
is neither convex nor concave:
First derivative with respect to b when a=1:
First derivative with respect to z when a=1:
Higher derivatives with respect to b when a=1:
Higher derivatives with respect to z when a=1 and b=2:
Plot the higher derivatives with respect to z when a=1 and b=2:
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:
Find series expansion for an arbitrary symbolic direction :
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:
Wolfram Research (1996), Hypergeometric1F1Regularized, Wolfram Language function, https://reference.wolfram.com/language/ref/Hypergeometric1F1Regularized.html (updated 2022).
Wolfram Language. 1996. "Hypergeometric1F1Regularized." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/Hypergeometric1F1Regularized.html.
Wolfram Language. (1996). Hypergeometric1F1Regularized. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Hypergeometric1F1Regularized.html