Category:Hypergeometric Series
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This category contains results about Hypergeometric Series.
Definitions specific to this category can be found in Definitions/Hypergeometric Series.
A hypergeometric series is a power series:
| \(\ds \map F {a, b, c; n}\) | \(=\) | \(\ds \sum_{n \mathop = 0}^\infty \alpha_n z^n\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \alpha_0 + \alpha_1 z + \alpha_2 z^2 + \cdots\) |
where:
- $\map F {a, b, c; n}$ denotes the Gaussian hypergeometric function
- $\alpha_n = \dfrac {a^{\overline n} b^{\overline n} } {c^{\overline n} \, n!}$
- $a^{\overline n}$ denotes the $n$th rising factorial of $a$.
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