Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm2d)

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=-21/8, b>=a

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

http://functions.wolfram.com/07.23.03.bm2d.01

Input Form

Hypergeometric2F1[-(21/8), 39/8, 23/4, z] == (1/(276758793 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (240240 + 44044 z + 68159 z^2 + 158678 z^3 + 748943 z^4 - 4233696 z^5 + 4958976 z^6 - 1757184 z^7 - (1/Sqrt[1 - z]) (240240 - 76076 z + 16107 z^2 + 104078 z^3 + 648947 z^4 - 13289264 z^5 + 29995392 z^6 - 24668160 z^7 + 7028736 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]