Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8um)

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=-13/8

http://functions.wolfram.com/07.23.03.b8um.01

Input Form

Hypergeometric2F1[-(41/8), -(13/8), 23/4, z] == (16 2^(3/4) (90200 - 1497320 z + 12857395 z^2 - 83853610 z^3 + 16563785293 z^4 + 27622369564 z^5 + 7340942013 z^6 - 144466842 z^7 + 11865291 z^8 - 588240 z^9 + (1/Sqrt[1 - z]) (4 (-22550 + 385605 z - 3398695 z^2 + 22525195 z^3 + 3805081037 z^4 + 1216024245 z^5 - 4255902285 z^6 - 832293423 z^7 + 51527373 z^8 - 4122582 z^9 + 196080 z^10))))/(509192306091 (1 + Sqrt[1 - z])^(3/4) 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]