Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8300)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=7/3, b>=a

For fixed z and a=7/3, b=11/3

http://functions.wolfram.com/07.23.03.8300.01

Input Form

Hypergeometric2F1[7/3, 11/3, -(9/2), -z] == ((13436928 + 167380992 z + 1004193792 z^2 + 4007327744 z^3 + 13258178560 z^4 + 62310600704 z^5 - 139576694569 z^6 + 29216182636 z^7 + 81822224 z^8) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-4478976 - 52641792 z - 298031104 z^2 - 1129926656 z^3 - 3645288448 z^4 + 52213839227 z^5 - 18579293516 z^6 + 81822224 z^7) Sinh[ArcSinh[Sqrt[z]]/3])/(13436928 (1 + z)^(21/2))

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]