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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=-5/2, a2>=-5/2
For fixed z and a1=-5/2, a2=1, a3>=1
For fixed z and a1=-5/2, a2=1, a3=1
For fixed z and a1=-5/2, a2=1, a3=1, b1=-3/2
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http://functions.wolfram.com/07.27.03.ab0s.01
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HypergeometricPFQ[{-(5/2), 1, 1}, {-(3/2), 7/2}, z] ==
-((I (-7680 I + 13120 I z + 96 I z^2 + 200 I z^3 + 900 I z^4 +
225 Pi^2 z^(9/2)))/(3072 z^2)) +
(5 Sqrt[1 - z] (128 - 176 z + 8 z^2 + 10 z^3 + 15 z^4) ArcSin[Sqrt[z]])/
(256 z^(5/2)) - (1/(110592 (-1 + z)^7))
(Sqrt[1 - z] (-258096 + 1440644 z - 2662126 z^2 + 10514939 z^3 -
7221306 z^4 + 9135930 z^5 - 9403290 z^6 + 6157035 z^7 - 2220390 z^8 +
337860 z^9) Log[1 - E^(I ArcSin[Sqrt[z]])]) +
(1/(110592 (-1 + z)^7)) (Sqrt[1 - z] (-258096 + 1440644 z - 2662126 z^2 +
10514939 z^3 - 7221306 z^4 + 9135930 z^5 - 9403290 z^6 + 6157035 z^7 -
2220390 z^8 + 337860 z^9) Log[(1 - E^(I ArcSin[Sqrt[z]]))/
(1 + E^(I ArcSin[Sqrt[z]]))]) - (75/256) z^(5/2) ArcSin[Sqrt[z]]
Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))] +
(1/(110592 (-1 + z)^7)) (Sqrt[1 - z] (-258096 + 1440644 z - 2662126 z^2 +
10514939 z^3 - 7221306 z^4 + 9135930 z^5 - 9403290 z^6 + 6157035 z^7 -
2220390 z^8 + 337860 z^9) Log[1 + E^(I ArcSin[Sqrt[z]])]) -
(75/256) I z^(5/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])] +
(75/256) I z^(5/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])]
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</annotation-xml> </semantics> </math>
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SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]]]], "-", RowBox[List[FractionBox["75", "256"], " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], "+", RowBox[List[FractionBox["75", "256"], " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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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,...,ap},{b1,...,bq},z] | |
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