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

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=-3/4

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

Input Form

Hypergeometric2F1[-(17/4), -(3/4), 9/2, -z] == (8 Sqrt[2] (-2 (20 + 266 z + 1959 z^2 + 16850 z^3 - 68286 z^4 + 16850 z^5 + 1959 z^6 + 266 z^7 + 20 z^8) + (40 + 552 z + 4179 z^2 + 35595 z^3 - 36358 z^4 - 66514 z^5 + 2023 z^6 + 271 z^7 + 20 z^8)/Sqrt[1 + z]))/ (1341153 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]