Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bad3)

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=-39/8, b>=a

For fixed z and a=-39/8, b=21/8

http://functions.wolfram.com/07.23.03.bad3.01

Input Form

Hypergeometric2F1[-(39/8), 21/8, 13/4, z] == (1/(5098555 z^3)) (4 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (14260 + 27807 z + 506943 z^2 - 2557003 z^3 + 4821465 z^4 - 4529952 z^5 + 2137344 z^6 - 405504 z^7 - (1/Sqrt[1 - z]) (14260 + 20677 z + 491257 z^2 - 3452161 z^3 + 8742911 z^4 - 11502064 z^5 + 8456064 z^6 - 3311616 z^7 + 540672 z^8)))

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]