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

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=-25/8, b>=a

For fixed z and a=-25/8, b=43/8

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

Input Form

Hypergeometric2F1[-(25/8), 43/8, 23/4, z] == (16 2^(3/4) (-4 (170 + 255 z + 510 z^2 + 1445 z^3 - 206268 z^4 + 555744 z^5 - 512512 z^6 + 159744 z^7) + (1/Sqrt[1 - z]) (680 + 680 z + 1445 z^2 + 4590 z^3 + 887037 z^4 - 3555552 z^5 + 5270272 z^6 - 3461120 z^7 + 851968 z^8)))/ (27445509 (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]