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

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=-23/8, b>=a

For fixed z and a=-23/8, b=45/8

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

Input Form

Hypergeometric2F1[-(23/8), 45/8, -(11/2), -z] == (1/(48345088 (1 + z)^(65/8))) ((-(-48345088 - 249142016 z - 433766688 z^2 - 202581327 z^3 + 88213476 z^4 - 116976314 z^5 + 516726756 z^6 + 2480744913 z^7 + 3609147552 z^8 + 2585507584 z^9 + 942436352 z^10 + 140574720 z^11)) Cos[ArcTan[Sqrt[z]]/4] + 4 Sqrt[z] (3021568 + 14627136 z + 22787301 z^2 + 6611826 z^3 - 6249152 z^4 + 9178442 z^5 + 107099379 z^6 + 184565724 z^7 + 144765984 z^8 + 56156672 z^9 + 8785920 z^10) Sin[ArcTan[Sqrt[z]]/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]