AppellF4
AppellF4[a,b,c1,c2,x,y]
is the Appell hypergeometric function of two variables .
Details
- AppellF4 belongs to the family of Appell functions that generalize the hypergeometric series and solves the system of Horn PDEs with polynomial coefficients.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- has a primary definition through the hypergeometric series , which is convergent inside the region .
- The region of convergence of the Appell F4 series for real values of its arguments is the following:
- In general, satisfies the following Horn PDE system »:
- reduces to when or .
- For certain special arguments, AppellF4 automatically evaluates to exact values.
- AppellF4 can be evaluated to arbitrary numerical precision.
Examples
open allclose allBasic Examples (7)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Plot a family of AppellF4 functions:
Series expansion at the origin:
TraditionalForm formatting:
Scope (17)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate AppellF4 efficiently at high precision:
Compute average-case statistical intervals using Around:
Compute the elementwise values of an array:
Or compute the matrix AppellF4 function using MatrixFunction:
Specific Values (3)
Visualization (3)
Differentiation (4)
Series Expansions (1)
Find the Taylor expansion using Series:
Applications (1)
Neat Examples (1)
Many elementary and special functions are special cases of AppellF4:
Text
Wolfram Research (2023), AppellF4, Wolfram Language function, https://reference.wolfram.com/language/ref/AppellF4.html.
CMS
Wolfram Language. 2023. "AppellF4." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AppellF4.html.
APA
Wolfram Language. (2023). AppellF4. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AppellF4.html