Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7t0)

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=-43/8, b>=a

For fixed z and a=-43/8, b=9/8

http://functions.wolfram.com/07.23.03.b7t0.01

Input Form

Hypergeometric2F1[-(43/8), 9/8, 13/4, z] == (4 2^(1/4) (-269610 + 1833348 z + 2681540 z^2 - 4285760 z^3 + 4067062 z^4 - 2321876 z^5 + 739584 z^6 - 101376 z^7 + (1/Sqrt[1 - z]) (269610 - 1968153 z + 9475712 z^2 - 21479598 z^3 + 27672718 z^4 - 22426769 z^5 + 11288096 z^6 - 3237120 z^7 + 405504 z^8)))/ (45097117 (1 + Sqrt[1 - z])^(1/4) z^2)

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]