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

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=-29/8, b>=a

For fixed z and a=-29/8, b=47/8

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

Input Form

Hypergeometric2F1[-(29/8), 47/8, -(17/4), z] == (1/(5042336 2^(1/4) (-1 + z)^6)) ((1 + Sqrt[1 - z])^(1/4) (2521168 - 2335788 z - 2999591 z^2 - 5087255 z^3 - 14320605 z^4 + 254533271 z^5 - 613009056 z^6 + 637325568 z^7 - 315617280 z^8 + 61276160 z^9 + (1/Sqrt[1 - z]) (2521168 - 3596372 z - 2146843 z^2 - 3453059 z^3 - 11354525 z^4 - 630317069 z^5 + 2538744396 z^6 - 4110813696 z^7 + 3397143552 z^8 - 1430978560 z^9 + 245104640 z^10)))

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]