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

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=-19/8

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

Input Form

Hypergeometric2F1[-(37/8), -(19/8), 11/2, -z] == -((1024 (Sqrt[z] Sqrt[1 + z] (-1442112 - 25743416 z - 244932637 z^2 - 1887555074 z^3 - 64142023675 z^4 + 206319192592 z^5 - 130013075299 z^6 + 14708715142 z^7 + 250293659 z^8 + 7372420 z^9) Cosh[(3 ArcSinh[Sqrt[z]])/4] + (1922816 + 35966960 z + 355831479 z^2 + 2794578069 z^3 + 32102897079 z^4 - 122990567751 z^5 - 37080556455 z^6 + 100953784671 z^7 - 14832940419 z^8 - 253979869 z^9 - 7372420 z^10) Sinh[(3 ArcSinh[Sqrt[z]])/4]))/ (42669456604775 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]