Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c4ed)

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=13/8, b>=a

For fixed z and a=13/8, b=25/8

http://functions.wolfram.com/07.23.03.c4ed.01

Input Form

Hypergeometric2F1[13/8, 25/8, -(19/4), z] == (-608 + 6160 z - 29046 z^2 + 86699 z^3 - 197328 z^4 + 492282 z^5 + 491358 z^6 + 2451 z^7 + (1/Sqrt[1 - z]) (2 (-304 + 3232 z - 16025 z^2 + 50245 z^3 - 118704 z^4 + 290850 z^5 + 1335327 z^6 + 164217 z^7 - 4902 z^8)))/ (608 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + z)^9)

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]