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Hypergeometric Functions
The generalized hypergeometric function (in Mathematica)
HypergeometricPFQ[{a1, a2, ..., ap}, {b1, b2, ..., bq}, z]
is defined by the following power series:
where the Pochhammer symbol (a)k is defined by:
Thomas Clausen (1801-1885) introduced this series in 1828 for
p = 3 and q = 2. Leo Pochhammer (1841-1920)
introduced the notation; Ernest William Barnes (1874-1953) modified
it later.
Various mathematical constants, all elementary functions, and many
special functions can be expressed in the hypergeometric notation:
Mathematica currently uses this last formula, due to the
Chudnovsky brothers, for calculating pi to arbitrary precision.
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