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8

Hypergeometric functions

Hypergeometric functions were introduced briefly in Chapters 1 and 3. The series representations of these functions, like the series representations of Kummer functions, are examples of a more general concept of hypergeometric series.

After a brief discussion of general hypergeometric series, we discuss solutions of the hypergeometric equation

 (8.0.1)

and the two classic transformations (Pfaff, Euler) from one solution to another.

There are three natural pairs of solutions of (8.0.1), normalized at the singular points x = 0, x = 1, and x = ∞ respectively. Any three solutions must satisfy a linear relation. ...

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