Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.0772)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a=-11/2, b>=a

For fixed z and a=-11/2, b=-7/2

http://functions.wolfram.com/07.23.03.0772.01

Input Form

Hypergeometric2F1[-(11/2), -(7/2), 11/2, -z] == (1/(8589934592 z^(9/2))) (Sqrt[z] Sqrt[1 + z] (-24255 + 2 z (-269115 + 4 z (-828597 + 2 z (-4383687 + 8 z (57282641 + 2 z (-82067551 + 4 z (14061259 + 2 z (-1146259 + 112 z (109 + 2 z))))))))) + 3465 (7 + 32 z (5 + 3 z (21 + 16 z (14 + z (245 + 16 z (-147 + z (-7 + 2 z) (-35 + 6 z))))))) ArcSinh[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]