AppellF1
AppellF1[a,b1,b2,c,x,y]
is the Appell hypergeometric function of two variables .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
has series expansion
.
reduces to
when
or
.
- For certain special arguments, AppellF1 automatically evaluates to exact values.
- AppellF1 can be evaluated to arbitrary numerical precision.
- AppellF1[a,b1,b2,c,x,y] has singular lines in two‐variable complex
space at
and
, and has branch cut discontinuities along the rays from
to
in
and
.
- FullSimplify and FunctionExpand include transformation rules for AppellF1.
Examples
open allclose allBasic Examples (8)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (25)
Numerical Evaluation (4)
The precision of the output tracks the precision of the input:
Evaluate AppellF1 efficiently at high precision:
Specific Values (4)
For simple parameters, AppellF1 evaluates to simpler functions:
Visualization (3)
Function Properties (9)
AppellF1 is not an analytic function:
It has both singularities and discontinuities:
is neither nondecreasing nor nonincreasing:
is neither non-negative nor non-positive:
is neither convex nor concave:
TraditionalForm formatting:
Differentiation (3)
Series Expansions (2)
Find the Taylor expansion using Series:
Applications (1)
Properties & Relations (2)
Evaluate integrals in terms of AppellF1:
Use FullSimplify to simplify some expressions involving AppellF1:
Text
Wolfram Research (1999), AppellF1, Wolfram Language function, https://reference.wolfram.com/language/ref/AppellF1.html.
CMS
Wolfram Language. 1999. "AppellF1." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AppellF1.html.
APA
Wolfram Language. (1999). AppellF1. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AppellF1.html