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

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=37/8, b>=a

For fixed z and a=37/8, b=41/8

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

Input Form

Hypergeometric2F1[37/8, 41/8, -(23/4), z] == (-307648 + 5902160 z - 56286648 z^2 + 364803065 z^3 - 1899522863 z^4 + 9492159885 z^5 - 68204994715 z^6 - 457442055285 z^7 - 432912419469 z^8 - 100652880417 z^9 - 4451046513 z^10 + (1/Sqrt[1 - z]) (-307648 + 6055984 z - 59199272 z^2 + 392227847 z^3 - 2075245432 z^4 + 10399616708 z^5 - 72734390872 z^6 - 1325178716790 z^7 - 1990446621384 z^8 - 769238764908 z^9 - 73287077376 z^10 - 804170649 z^11))/(307648 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + z)^15)

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]