# 15. Hypergeometric Function

$F\left(a,b;c;x\right)$ denotes the hypergeometric function $F$ (also known as the generalized hypergeometric function ${}_{2}F_{1}\left(a,b;c;x\right)$); see DLMF (15.2.1).
This function is not defined when $c$ is a non-positive integer. Computations are for real $a,b,c$ and $x$, which currently must satisfy all of the conditions:
• $|x|<1$,
• either $a$ or $b$ must be integer,
• if $a,b$ are non-negative integers and $c$ is an integer, then $c>\mathrm{min}\left(a,b\right)$,
• if $a,c$ are integers but $b$ is not, then $c>a$,
• if $b,c$ are integers but $a$ is not, then $c>b$.
Evaluate $F\left(a,b;c;x\right)$ as a Tabulation or Comparison?
Get function arguments from form or data file?
Specify the data file to compare tofor arguments:
Note: The lines in the data file must contain values for $a$, $b$, $c$, $x$ and $F\left(a,b;c;x\right)$ in that order, separated by commas or spaces.
Specify grid for function parameters and arguments:
Choose $a$ starting from ending with stepping by
Choose $b$ starting from ending with stepping by
Choose $c$ starting from ending with stepping by
Choose $x$ starting from ending with stepping by
Show output to digits, the number of digits in file, using
Return unformatted output only