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

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=47/8

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, 23/4, z] == (1/(278142586965 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (1321936 + 3635324 z + 11769737 z^2 + 51965390 z^3 + 459322329 z^4 - 5886186108 z^5 + 16812077568 z^6 - 20977499136 z^7 + 12316508160 z^8 - 2794192896 z^9 - (1/Sqrt[1 - z]) (1321936 + 2974356 z + 9786833 z^2 + 45543485 z^3 + 431589571 z^4 - 14815212549 z^5 + 64570867152 z^6 - 121337128704 z^7 + 116863549440 z^8 - 56950063104 z^9 + 11176771584 z^10)))

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]