Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ahz3)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=3, a₃>=3

For fixed z and a₁=-3/2, a₂=3, a₃=3

For fixed z and a₁=-3/2, a₂=3, a₃=3, b₁=3/2

http://functions.wolfram.com/07.27.03.ahz3.01

Input Form

HypergeometricPFQ[{-(3/2), 3, 3}, {3/2, 5/2}, z] == (I (96 I + 648 Pi^2 Sqrt[z] - 22600 I z - 8100 Pi^2 z^(3/2) + 44100 I z^2 + 11025 Pi^2 z^(5/2)))/(32768 z) - (3 Sqrt[1 - z] (8 + 626 z - 3925 z^2 + 3675 z^3) ArcSin[Sqrt[z]])/ (8192 (-1 + z) z^(3/2)) + (1/(24576 (-1 + z)^6)) (Sqrt[1 - z] (-49512 + 419604 z - 1563173 z^2 + 3130700 z^3 - 3675747 z^4 + 2543928 z^5 - 964560 z^6 + 154980 z^7) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(24576 (-1 + z)^6)) (Sqrt[1 - z] (49512 - 419604 z + 1563173 z^2 - 3130700 z^3 + 3675747 z^4 - 2543928 z^5 + 964560 z^6 - 154980 z^7) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) + (9 (72 - 900 z + 1225 z^2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (8192 Sqrt[z]) - (1/(24576 (-1 + z)^6)) (Sqrt[1 - z] (-49512 + 419604 z - 1563173 z^2 + 3130700 z^3 - 3675747 z^4 + 2543928 z^5 - 964560 z^6 + 154980 z^7) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (9 I (72 - 900 z + 1225 z^2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (8192 Sqrt[z]) - (9 I (72 - 900 z + 1225 z^2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(8192 Sqrt[z])

Standard Form

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MathML Form

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<apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3675 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3925 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 626 </cn> <ci> z </ci> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> 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RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], RowBox[List["8192", " ", SqrtBox["z"]]]], "-", FractionBox[RowBox[List["9", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["72", "-", RowBox[List["900", " ", "z"]], "+", RowBox[List["1225", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]], RowBox[List["8192", " ", SqrtBox["z"]]]]]]]]]]

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},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},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]