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

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=-23/8, b>=a

For fixed z and a=-23/8, b=45/8

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

Input Form

Hypergeometric2F1[-(23/8), 45/8, 11/2, z] == (1/(377207225967 z^(9/2))) (512 ((1 + Sqrt[z])^(11/4) (206080 - 566720 Sqrt[z] + 1551120 z - 3025880 z^(3/2) + 6261037 z^2 - 10893168 z^(5/2) + 21715680 z^3 - 37403520 z^(7/2) + 102009600 z^4 + 164296704 z^(9/2) - 982265856 z^5 + 1159741440 z^(11/2) - 421724160 z^6) + (1 - Sqrt[z])^(11/4) (-206080 - 566720 Sqrt[z] - 1551120 z - 3025880 z^(3/2) - 6261037 z^2 - 10893168 z^(5/2) - 21715680 z^3 - 37403520 z^(7/2) - 102009600 z^4 + 164296704 z^(9/2) + 982265856 z^5 + 1159741440 z^(11/2) + 421724160 z^6)))

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]