Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7n1)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-7/8

http://functions.wolfram.com/07.23.03.b7n1.01

Input Form

Hypergeometric2F1[-(43/8), -(7/8), 21/4, z] == (16 2^(1/4) (4 (191178 - 2889729 z + 22764888 z^2 - 144410469 z^3 + 6260526168 z^4 + 7102049141 z^5 - 34654840 z^6 + 6095265 z^7 - 815490 z^8 + 55760 z^9) + (1/Sqrt[1 - z]) (-764712 + 11941272 z - 96743421 z^2 + 621774582 z^3 + 8414792733 z^4 - 4709079364 z^5 - 4768758995 z^6 + 620490310 z^7 - 106421445 z^8 + 13661200 z^9 - 892160 z^10)))/(539760455355 (1 + Sqrt[1 - z])^(1/4) 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]