Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aaq8)

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

http://functions.wolfram.com/07.23.03.aaq8.01

Input Form

Hypergeometric2F1[-(17/4), 3, 23/4, z] == (1/(45097156608 z^(19/4))) (209 (2 z^(3/4) (-1276275 + 4813380 z - 3898440 z^2 - 3248700 z^3 + 101455242 z^4 - 198482004 z^5 + 171061072 z^6 - 72121140 z^7 + 12182625 z^8) + 69615 (-1 + z)^7 (55 + 154 z + 175 z^2) ArcTan[z^(1/4)] - 69615 (-1 + z)^7 (55 + 154 z + 175 z^2) ArcTanh[z^(1/4)]))

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]