Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aad5)

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=-7/4

http://functions.wolfram.com/07.23.03.aad5.01

Input Form

Hypergeometric2F1[-(17/4), -(7/4), 9/2, -z] == (8 Sqrt[2] (-40 - 656 z - 6305 z^2 - 78309 z^3 + 530706 z^4 - 427834 z^5 + 40691 z^6 + 1855 z^7 + 84 z^8 + (1/Sqrt[1 + z]) (40 + 676 z + 6628 z^2 + 81382 z^3 - 240834 z^4 - 168256 z^5 + 147072 z^6 - 938 z^7 - 42 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]