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

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=-29/8, b>=a

For fixed z and a=-29/8, b=-17/8

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

Input Form

Hypergeometric2F1[-(29/8), -(17/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (210010112 - 3210037376 z + 24869605371 z^2 - 140265951202 z^3 + 814117869565 z^4 + 23766826302660 z^5 + 25047100483685 z^6 + 4228392133630 z^7 + 780078915 z^8) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (210010112 - 3210037376 z + 24869605371 z^2 - 140265951202 z^3 + 814117869565 z^4 + 23766826302660 z^5 + 25047100483685 z^6 + 4228392133630 z^7 + 780078915 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (210010112 - 3210037376 z + 24869605371 z^2 - 140265951202 z^3 + 814117869565 z^4 + 23766826302660 z^5 + 25047100483685 z^6 + 4228392133630 z^7 + 780078915 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (210010112 - 3288791168 z + 26051835147 z^2 - 149274339058 z^3 + 864334871257 z^4 + 4410599712960 z^5 - 2162192276755 z^6 - 2793761530490 z^7 - 195799807665 z^8 + 3120315660 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (4997531405238597225 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)

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]