Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8959)

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=-23/4, b>=a

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

http://functions.wolfram.com/07.23.03.8959.01

Input Form

Hypergeometric2F1[-(23/4), -(23/4), 9/2, z] == (16 (-8 (-441138390 + 15042819099 z - 340676473984 z^2 + 11961143943364 z^3 + 219602769499476 z^4 + 765668798318930 z^5 + 866444959314928 z^6 + 344084759598372 z^7 + 42756172453778 z^8 + 1057529535787 z^9) EllipticE[(1/2) (1 - Sqrt[z])] + 8 (-441138390 + 15042819099 z - 340676473984 z^2 + 11961143943364 z^3 + 219602769499476 z^4 + 765668798318930 z^5 + 866444959314928 z^6 + 344084759598372 z^7 + 42756172453778 z^8 + 1057529535787 z^9) EllipticE[(1/2) (1 + Sqrt[z])] + (-1764553560 - 882276780 Sqrt[z] + 60171276396 z + 30012115133 z^(3/2) - 1362705895936 z^2 - 678882572984 z^(5/2) + 47844575773456 z^3 + 154342689188556 z^(7/2) + 878411077997904 z^4 + 1383497781971360 z^(9/2) + 3062675193275720 z^5 + 3408924425655310 z^(11/2) + 3465779837259712 z^6 + 3000350823563736 z^(13/2) + 1376339038393488 z^7 + 960528381253772 z^(15/2) + 171024689815112 z^8 + 96210542716012 z^(17/2) + 4230118143148 z^9 + 1795339871325 z^(19/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (1764553560 - 882276780 Sqrt[z] - 60171276396 z + 30012115133 z^(3/2) + 1362705895936 z^2 - 678882572984 z^(5/2) - 47844575773456 z^3 + 154342689188556 z^(7/2) - 878411077997904 z^4 + 1383497781971360 z^(9/2) - 3062675193275720 z^5 + 3408924425655310 z^(11/2) - 3465779837259712 z^6 + 3000350823563736 z^(13/2) - 1376339038393488 z^7 + 960528381253772 z^(15/2) - 171024689815112 z^8 + 96210542716012 z^(17/2) - 4230118143148 z^9 + 1795339871325 z^(19/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)/ (2087615215954125 Pi^(3/2) z^(7/2))

Standard Form

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MathML Form

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RowBox[List["171024689815112", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["96210542716012", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "-", RowBox[List["4230118143148", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["1795339871325", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["2087615215954125", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]]]]]

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]