AppellF2
AppellF2[a,b1,b2,c1,c2,x,y]
is the Appell hypergeometric function of two variables .
Details

- AppellF2 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 F2 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, AppellF2 automatically evaluates to exact values.
- AppellF2 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 AppellF2 functions:
Series expansion at the origin:
TraditionalForm formatting:
Scope (15)
Applications (1)
Neat Examples (1)
Many elementary and special functions are special cases of AppellF2:
Text
Wolfram Research (2023), AppellF2, Wolfram Language function, https://reference.wolfram.com/language/ref/AppellF2.html.
CMS
Wolfram Language. 2023. "AppellF2." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AppellF2.html.
APA
Wolfram Language. (2023). AppellF2. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AppellF2.html