Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9j2)

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=-41/8, b>=a

For fixed z and a=-41/8, b=43/8

http://functions.wolfram.com/07.23.03.b9j2.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, -(17/4), z] == (2 (604656 + 1387152 z + 3493701 z^2 + 11001228 z^3 + 53741709 z^4 + 1109091522 z^5 - 5527094144 z^6 + 9069046272 z^7 - 6372720640 z^8 + 1651113984 z^9) + (1/Sqrt[1 - z]) (1209312 + 2169648 z + 5449086 z^2 + 18086385 z^3 + 95388132 z^4 + 2161112877 z^5 - 14989716368 z^6 + 34906203904 z^7 - 38552616960 z^8 + 20754792448 z^9 - 4402970624 z^10))/ (1209312 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + 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]