Hypergeometric Differential Equation - The Hypergeometric Series

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:

(q)_n = \begin{cases} 1 & n = 0 \\ q(q+1) \cdots (q+n-1) & n > 0. \end{cases}

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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