Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab2o)

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=-15/4, b>=a

For fixed z and a=-15/4, b=-13/4

http://functions.wolfram.com/07.23.03.ab2o.01

Input Form

Hypergeometric2F1[-(15/4), -(13/4), 9/2, -z] == (8 Sqrt[2] (-4 (10 + 197 z + 2369 z^2 + 39270 z^3 - 381612 z^4 + 544489 z^5 - 183167 z^6 + 11276 z^7) + (1/Sqrt[1 + z]) (40 + 808 z + 9865 z^2 + 161722 z^3 - 843117 z^4 - 18172 z^5 + 783807 z^6 - 189830 z^7 + 3933 z^8)))/ (9694845 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]