Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9771)

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=11/4

http://functions.wolfram.com/07.23.03.9771.01

Input Form

Hypergeometric2F1[-(23/4), 11/4, -(1/2), -z] == (1/(34 Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z/(2 + 2 z)] (-42240 z^6 + 17 (1 + Sqrt[1 + z]) + 704 z^5 (-233 + 30 Sqrt[1 + z]) + 176 z^4 (-1393 + 376 Sqrt[1 + z]) + z (-6540 + 5469 Sqrt[1 + z]) + 8 z^3 (-21721 + 9284 Sqrt[1 + z]) + z^2 (-56949 + 34656 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]