Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bct4)

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=-35/8, b>=a

For fixed z and a=-35/8, b=9/8

http://functions.wolfram.com/07.23.03.bct4.01

Input Form

Hypergeometric2F1[-(35/8), 9/8, 17/4, z] == (8 2^(1/4) (112860 - 805695 z + 2375076 z^2 + 1546694 z^3 - 1525784 z^4 + 884833 z^5 - 284240 z^6 + 39168 z^7 + (1/Sqrt[1 - z]) (-112860 + 862125 z - 2763816 z^2 + 6918830 z^3 - 10133496 z^4 + 8449357 z^5 - 4308140 z^6 + 1244672 z^7 - 156672 z^8)))/ (58973153 (1 + Sqrt[1 - z])^(1/4) z^3)

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]