The Hypergeometric Series
The hypergeometric function is defined for |z| < 1 by the power series
provided that c does not equal 0, −1, −2, ... . Here (q)n is the (rising) Pochhammer symbol, which is defined by:
The series terminates if either a or b is a nonpositive integer. For complex arguments z with |z| ≥ 1 it can be analytically continued along any path in the complex plane that avoids the branch points 0 and 1.
Read more about this topic: Hypergeometric Differential Equation
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