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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-37/8, b>=a

For fixed z and a=-37/8, b=-17/8

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

Input Form

Hypergeometric2F1[-(37/8), -(17/8), 19/4, z] == (1/(324681477333 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-165242 + 2966845 z - 30551529 z^2 + 335277091 z^3 + 7669051949 z^4 + 11840948091 z^5 + 3195952929 z^6 - 2580347 z^7 + 100533 z^8) + (1/Sqrt[1 - z]) (660968 - 12197864 z + 128057185 z^2 - 1400769310 z^3 - 9727621153 z^4 + 1243724132 z^5 + 8676592239 z^6 + 1132336690 z^7 - 42391415 z^8 + 1608528 z^9)))

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]