Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aal2)

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=-17/4, b>=a

For fixed z and a=-17/4, b=5/4

http://functions.wolfram.com/07.23.03.aal2.01

Input Form

Hypergeometric2F1[-(17/4), 5/4, 9/2, -z] == (8 Sqrt[2] (2 (4420 + 31382 z + 90389 z^2 + 92820 z^3 + 218454 z^4 + 212542 z^5 + 120025 z^6 + 37520 z^7 + 5040 z^8) - (1/Sqrt[1 + z]) (8840 + 67184 z + 211055 z^2 + 268736 z^3 + 259242 z^4 + 238252 z^5 + 128775 z^6 + 38780 z^7 + 5040 z^8)))/ (4023459 z^(7/2) 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]