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

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=-3/8

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

Input Form

Hypergeometric2F1[-(37/8), -(3/8), 11/2, -z] == (1024 ((-Sqrt[z]) Sqrt[1 + z] (-1442112 - 18223832 z - 114123207 z^2 - 517502535 z^3 - 6350777026 z^4 + 5731968138 z^5 + 586186533 z^6 + 116621845 z^7 + 17582580 z^8 + 1334736 z^9) Cosh[(3 ArcSinh[Sqrt[z]])/4] + (-1922816 - 25940848 z - 172854935 z^2 - 819199018 z^3 - 4560384125 z^4 + 1587456464 z^5 + 6011530447 z^6 + 642383054 z^7 + 125246293 z^8 + 18249948 z^9 + 1334736 z^10) Sinh[(3 ArcSinh[Sqrt[z]])/4]))/(3449870959535 z^(9/2) 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]