Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc7s)

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=-37/8, b>=a

For fixed z and a=-37/8, b=39/8

http://functions.wolfram.com/07.23.03.bc7s.01

Input Form

Hypergeometric2F1[-(37/8), 39/8, 19/4, z] == (1/(352313943489 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (8592584 + 28902328 z + 129795445 z^2 + 1158185470 z^3 - 14944419219 z^4 + 42855720864 z^5 - 53624093952 z^6 + 31550238720 z^7 - 7169310720 z^8 - (1/Sqrt[1 - z]) (4 (2148146 + 6151509 z + 28567552 z^2 + 272284480 z^3 - 9390374974 z^4 + 41082008631 z^5 - 77417731776 z^6 + 74726775552 z^7 - 36479139840 z^8 + 7169310720 z^9))))

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]