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
Famous quotes containing the word series:
“Through a series of gradual power losses, the modern parent is in danger of losing sight of her own child, as well as her own vision and style. Its a very big price to pay emotionally. Too bad its often accompanied by an equally huge price financially.”
—Sonia Taitz (20th century)