Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7q8)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=19/4

http://functions.wolfram.com/07.23.03.a7q8.01

Input Form

Hypergeometric2F1[-(23/4), 19/4, -(11/2), -z] == (Sqrt[z] (12899328 z^10 + 22176 (1 + Sqrt[1 + z]) - 1008 z (13 + 24 Sqrt[1 + z]) - 169728 z^9 (-317 + 38 Sqrt[1 + z]) - 49920 z^8 (-1685 + 442 Sqrt[1 + z]) + 14 z^2 (1127 + 2189 Sqrt[1 + z]) - 99 z^5 (2071 + 2614 Sqrt[1 + z]) - 624 z^7 (-93107 + 41526 Sqrt[1 + z]) - z^3 (26405 + 46138 Sqrt[1 + z]) + z^4 (59768 + 89046 Sqrt[1 + z]) - 12 z^6 (-1216225 + 899392 Sqrt[1 + z])))/(44352 Sqrt[2] (1 + z)^(9/2) Sqrt[-1 + 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]