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

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=35/8, b>=a

For fixed z and a=35/8, b=47/8

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

Input Form

Hypergeometric2F1[35/8, 47/8, -(21/4), z] == (1/(1315392 2^(1/4) (-1 + z)^15)) ((1 + Sqrt[1 - z])^(1/4) (-657696 + 13044304 z - 130555074 z^2 + 911519443 z^3 - 5383771085 z^4 + 34789186575 z^5 + 974296652747 z^6 + 1607106677913 z^7 + 641059633449 z^8 + 55767105525 z^9 + 38159099 z^10 + (1/Sqrt[1 - z]) (2 (-328848 + 6686576 z - 68497507 z^2 + 487603774 z^3 - 2912000500 z^4 + 18687400160 z^5 - 1188885720946 z^6 - 3122367752196 z^7 - 1981662311268 z^8 - 332014863360 z^9 - 8280524483 z^10 + 76318198 z^11))))

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]