Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm75)

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=-21/8, b>=a

For fixed z and a=-21/8, b=47/8

http://functions.wolfram.com/07.23.03.bm75.01

Input Form

Hypergeometric2F1[-(21/8), 47/8, -(5/4), z] == (1/(14260 2^(1/4) (-1 + z)^4)) ((1 + Sqrt[1 - z])^(1/4) (2 (3565 + 29946 z - 1400463 z^2 + 5374536 z^3 - 8027712 z^4 + 5372928 z^5 - 1351680 z^6) + (1/Sqrt[1 - z]) (7130 + 56327 z + 6090708 z^2 - 36931989 z^3 + 84050400 z^4 - 92885760 z^5 + 50417664 z^6 - 10813440 z^7)))

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]