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

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=21/8

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

Input Form

Hypergeometric2F1[-(15/8), 21/8, 21/4, z] == (1/(15785 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (144 - 468 z + 389 z^2 + 90 z^3 + 525 z^4 - 616 z^5 + 192 z^6 + (-144 + 540 z - 605 z^2 + 55 z^3 - 455 z^4 + 1393 z^5 - 1040 z^6 + 256 z^7)/Sqrt[1 - z]))

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]