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

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=-17/4, b>=a

For fixed z and a=-17/4, b=11/2

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

Input Form

Hypergeometric2F1[-(17/4), 11/2, 5, z] == (128 Sqrt[2] (2 (-56576 - 240448 z - 1089972 z^2 - 7858760 z^3 + 330451325 z^4 - 1264658772 z^5 + 1904062314 z^6 - 1289295084 z^7 + 328582485 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-56576 - 240448 z - 1089972 z^2 - 7858760 z^3 + 330451325 z^4 - 1264658772 z^5 + 1904062314 z^6 - 1289295084 z^7 + 328582485 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (56576 + 268736 z + 1233180 z^2 + 8521760 z^3 - 143805775 z^4 + 365332437 z^5 - 341099913 z^6 + 109527495 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-56576 - 240448 z - 1089972 z^2 - 7858760 z^3 + 330451325 z^4 - 1264658772 z^5 + 1904062314 z^6 - 1289295084 z^7 + 328582485 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-56576 - 240448 z - 1089972 z^2 - 7858760 z^3 + 330451325 z^4 - 1264658772 z^5 + 1904062314 z^6 - 1289295084 z^7 + 328582485 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-56576 - 240448 z - 1089972 z^2 - 7858760 z^3 + 330451325 z^4 - 1264658772 z^5 + 1904062314 z^6 - 1289295084 z^7 + 328582485 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (11658772125 Pi Sqrt[1 + Sqrt[1 - z]] z^4)

Standard Form

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MathML Form

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<mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 328582485 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1289295084 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1904062314 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1264658772 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 330451325 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 7858760 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1089972 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 240448 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - 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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]