Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.blot)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-21/8, b>=a

For fixed z and a=-21/8, b=21/8

http://functions.wolfram.com/07.23.03.blot.01

Input Form

Hypergeometric2F1[-(21/8), 21/8, -(9/2), -z] == (1/3072) ((1/(1 + z)^4) (2 (1536 + 4224 z + 2730 z^2 - 553 z^3 + 428 z^4 - 801 z^5 - 1968 z^6 - 816 z^7) Cosh[(3 ArcSinh[Sqrt[z]])/4]) + (1/(1 + z)^(9/2)) (Sqrt[z] (-2304 - 6672 z - 4809 z^2 + 660 z^3 - 445 z^4 + 3366 z^5 + 4752 z^6 + 1632 z^7) Sinh[(3 ArcSinh[Sqrt[z]])/4]))

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]