Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9657)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=7/4

http://functions.wolfram.com/07.23.03.9657.01

Input Form

Hypergeometric2F1[-(23/4), 7/4, 5/2, -z] == (2 Sqrt[2] (9614 - 33649 z - 216919 z^2 - 512859 z^3 - 642395 z^4 - 454728 z^5 - 172656 z^6 - 27456 z^7 + (1/Sqrt[1 + z]) (2 (-4807 + 14421 z + 177557 z^2 + 572627 z^3 + 971094 z^4 + 973508 z^5 + 582504 z^6 + 193248 z^7 + 27456 z^8))))/ (480675 z^(3/2) Sqrt[-1 + Sqrt[1 + 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]