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

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=-15/8, b>=a

For fixed z and a=-15/8, b=39/8

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

Input Form

Hypergeometric2F1[-(15/8), 39/8, -(11/2), z] == (1/(96374784 (1 - z)^(17/2))) (Sqrt[1 - z] (96374784 - 613841664 z + 1526732640 z^2 - 1693049159 z^3 + 444059252 z^4 + 410190326 z^5 + 1031120636 z^6 - 2435305015 z^7 + 1983360808 z^8 - 760194864 z^9 + 115983296 z^10) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (24093696 - 160989696 z + 426439596 z^2 - 524021489 z^3 + 203213556 z^4 + 101606778 z^5 + 2043834624 z^6 - 3339210017 z^7 + 2348960328 z^8 - 818186512 z^9 + 115983296 z^10) Sin[ArcSin[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]