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

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=31/8, b>=a

For fixed z and a=31/8, b=43/8

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

Input Form

Hypergeometric2F1[31/8, 43/8, -(21/4), z] == (12096 - 219600 z + 1988136 z^2 - 12360069 z^3 + 63600495 z^4 - 346768401 z^5 + 5547789555 z^6 + 14120359649 z^7 + 7082153309 z^8 + 722220485 z^9 + 314265 z^10 + (1/Sqrt[1 - z]) (12096 - 225648 z + 2096424 z^2 - 13327443 z^3 + 69545265 z^4 - 377139651 z^5 + 5713924293 z^6 + 17632138051 z^7 + 11355134483 z^8 + 1817974095 z^9 + 39073615 z^10 - 419020 z^11))/(12096 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^14)

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]