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

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=-37/8, b>=a

For fixed z and a=-37/8, b=47/8

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, -(21/4), z] == ((1 + Sqrt[1 - z])^(1/4) (2 (52944528 - 40338688 z - 47911461 z^2 - 68964925 z^3 - 131167045 z^4 - 417021579 z^5 + 8505569314 z^6 - 21547565952 z^7 + 23173286400 z^8 - 11765022720 z^9 + 2328494080 z^10) + (1/Sqrt[1 - z]) (105889056 - 133621904 z - 68720366 z^2 - 86551783 z^3 - 180485255 z^4 - 679389893 z^5 - 41330167583 z^6 + 174617293488 z^7 - 292849556736 z^8 + 248565841920 z^9 - 106926899200 z^10 + 18627952640 z^11)))/ (211778112 2^(1/4) (-1 + z)^6)

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]