AppellF3
AppellF3[a1,a2,b1,b2,c,x,y]
is the Appell hypergeometric function of two variables .
Details
- AppellF3 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 F3 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, AppellF3 automatically evaluates to exact values.
- AppellF3 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 AppellF3 functions:
Series expansion at the origin:
TraditionalForm formatting:
Scope (15)
Applications (1)
Neat Examples (1)
Many elementary and special functions are special cases of AppellF3:
Text
Wolfram Research (2023), AppellF3, Wolfram Language function, https://reference.wolfram.com/language/ref/AppellF3.html.
CMS
Wolfram Language. 2023. "AppellF3." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AppellF3.html.
APA
Wolfram Language. (2023). AppellF3. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AppellF3.html