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

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=-37/8, b>=a

For fixed z and a=-37/8, b=-15/8

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

Input Form

Hypergeometric2F1[-(37/8), -(15/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (35160064 - 562423680 z + 4608787155 z^2 - 27976447030 z^3 + 180527748765 z^4 + 1663172746880 z^5 + 1188588525885 z^6 + 80097657090 z^7 - 3857618765 z^8 + 154820820 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (35160064 - 562423680 z + 4608787155 z^2 - 27976447030 z^3 + 180527748765 z^4 + 1663172746880 z^5 + 1188588525885 z^6 + 80097657090 z^7 - 3857618765 z^8 + 154820820 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (35160064 - 584398720 z + 4956696675 z^2 - 30800958580 z^3 + 197566452265 z^4 - 3500816937610 z^5 - 6935640083435 z^6 - 2073246946800 z^7 - 650616065 z^8 + 25803470 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (35160064 - 562423680 z + 4608787155 z^2 - 27976447030 z^3 + 180527748765 z^4 + 1663172746880 z^5 + 1188588525885 z^6 + 80097657090 z^7 - 3857618765 z^8 + 154820820 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (1324829307221034615 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]