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

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=45/8

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

Input Form

Hypergeometric2F1[35/8, 45/8, -(7/2), z] == -((1/(824064 (1 - z)^(27/2))) (Sqrt[1 - z] (-824064 + 16738800 z - 185443371 z^2 + 1719409536 z^3 - 25892667081 z^4 - 182767066194 z^5 - 217626443645 z^6 - 63921386236 z^7 - 3354082479 z^8 + 19905534 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] + 2 Sqrt[z] (-309024 + 6322116 z - 70428501 z^2 + 654367977 z^3 - 30632530333 z^4 - 132166236879 z^5 - 129885168279 z^6 - 34228525021 z^7 - 1682017623 z^8 + 9952767 z^9) Sin[(3 ArcSin[Sqrt[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]