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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-7/2, b>=a

For fixed z and a=-7/2, b=-9/4

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

Input Form

Hypergeometric2F1[-(7/2), -(9/4), 6, z] == (32 Sqrt[2] (2 (32768 - 500736 z + 3882816 z^2 - 21966880 z^3 + 128493600 z^4 + 2435928096 z^5 + 2340475748 z^6 + 361105602 z^7 + 480675 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (32768 - 500736 z + 3882816 z^2 - 21966880 z^3 + 128493600 z^4 + 2435928096 z^5 + 2340475748 z^6 + 361105602 z^7 + 480675 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-32768 + 484352 z - 3645760 z^2 + 20217120 z^3 - 118918400 z^4 - 958807616 z^5 - 632368516 z^6 - 56719650 z^7 + 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (32768 - 500736 z + 3882816 z^2 - 21966880 z^3 + 128493600 z^4 + 2435928096 z^5 + 2340475748 z^6 + 361105602 z^7 + 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (32768 - 500736 z + 3882816 z^2 - 21966880 z^3 + 128493600 z^4 + 2435928096 z^5 + 2340475748 z^6 + 361105602 z^7 + 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (32768 - 500736 z + 3882816 z^2 - 21966880 z^3 + 128493600 z^4 + 2435928096 z^5 + 2340475748 z^6 + 361105602 z^7 + 480675 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (24538939425 Pi Sqrt[1 + Sqrt[1 - z]] z^5)

Standard Form

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MathML 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]