Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6cp)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-19/8

http://functions.wolfram.com/07.23.03.b6cp.01

Input Form

Hypergeometric2F1[-(45/8), -(19/8), 9/2, -z] == -((256 (Sqrt[z] Sqrt[1 + z] (-257520 - 5503417 z - 72515486 z^2 - 4367353887 z^3 + 20056103476 z^4 - 18467540815 z^5 + 3182673714 z^6 + 93060047 z^7 + 6166024 z^8 + 268088 z^9) Cosh[(3 ArcSinh[Sqrt[z]])/4] - 4 (-85840 - 1907794 z - 25735905 z^2 - 466204551 z^3 + 3022469529 z^4 - 496709891 z^5 - 3176876977 z^6 + 807112435 z^7 + 24027387 z^8 + 1575017 z^9 + 67022 z^10) Sinh[(3 ArcSinh[Sqrt[z]])/4]))/(775808301905 z^(7/2) Sqrt[1 + z]))

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]