Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8yc)

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=-21/4, b>=a

For fixed z and a=-21/4, b=23/4

http://functions.wolfram.com/07.23.03.a8yc.01

Input Form

Hypergeometric2F1[-(21/4), 23/4, -(7/2), z] == (1/(1404480 Pi^(3/2))) (((1/(-1 + z)^4) (2 (351120 + 1667820 z + 7594433 z^2 + 45560746 z^3 + 666949305 z^4 - 7217983520 z^5 + 21089146880 z^6 - 27503099904 z^7 + 16936599552 z^8 - 4026531840 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) + (1/(-1 + z)^4) (2 (351120 + 1667820 z + 7594433 z^2 + 45560746 z^3 + 666949305 z^4 - 7217983520 z^5 + 21089146880 z^6 - 27503099904 z^7 + 16936599552 z^8 - 4026531840 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3)) ((-351120 + 175560 Sqrt[z] - 1843380 z + 994840 z^(3/2) - 8589273 z^2 + 4715249 z^(5/2) - 50275995 z^3 + 27139695 z^(7/2) - 694089000 z^4 + 1709634080 z^(9/2) + 5508349440 z^5 - 9389987840 z^(11/2) - 11699159040 z^6 + 17537433600 z^(13/2) + 9965666304 z^7 - 13916700672 z^(15/2) - 3019898880 z^8 + 4026531840 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) ((351120 + 175560 Sqrt[z] + 1843380 z + 994840 z^(3/2) + 8589273 z^2 + 4715249 z^(5/2) + 50275995 z^3 + 27139695 z^(7/2) + 694089000 z^4 + 1709634080 z^(9/2) - 5508349440 z^5 - 9389987840 z^(11/2) + 11699159040 z^6 + 17537433600 z^(13/2) - 9965666304 z^7 - 13916700672 z^(15/2) + 3019898880 z^8 + 4026531840 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

Standard Form

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MathML Form

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Rule Form

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RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["8589273", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4715249", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["50275995", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["27139695", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["694089000", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1709634080", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["5508349440", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["9389987840", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["11699159040", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["17537433600", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["9965666304", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["13916700672", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["3019898880", " ", SuperscriptBox["z", 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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]