Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6638)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=1, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=1

For fixed z and a₁=-7/2, a₂=1, a₃=1, b₁=-5/2

http://functions.wolfram.com/07.27.03.6638.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 1}, {-(5/2), 3/2}, z] == -((I (2880 I + 4704 I z + 9800 I z^2 + 44100 I z^3 + 11025 Pi^2 z^(7/2)))/ 23040) + (7 Sqrt[1 - z] (48 + 56 z + 70 z^2 + 105 z^3) ArcSin[Sqrt[z]])/ (384 Sqrt[z]) - (1/(245760 (-1 + z)^7)) (Sqrt[1 - z] (-245760 + 1259704 z - 2701676 z^2 + 2233704 z^3 + 5010089 z^4 - 25533361 z^5 + 51025905 z^6 - 57480255 z^7 + 37812530 z^8 - 13586440 z^9 + 2066960 z^10) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(245760 (-1 + z)^7)) (Sqrt[1 - z] (-245760 + 1259704 z - 2701676 z^2 + 2233704 z^3 + 5010089 z^4 - 25533361 z^5 + 51025905 z^6 - 57480255 z^7 + 37812530 z^8 - 13586440 z^9 + 2066960 z^10) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) - (245/128) z^(7/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))] + (1/(245760 (-1 + z)^7)) (Sqrt[1 - z] (-245760 + 1259704 z - 2701676 z^2 + 2233704 z^3 + 5010089 z^4 - 25533361 z^5 + 51025905 z^6 - 57480255 z^7 + 37812530 z^8 - 13586440 z^9 + 2066960 z^10) Log[1 + E^(I ArcSin[Sqrt[z]])]) - (245/128) I z^(7/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])] + (245/128) I z^(7/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])]

Standard Form

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MathML Form

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"1"]], "+", "z"]], ")"]], "7"]]]], "-", RowBox[List[FractionBox["245", "128"], " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", SqrtBox["z"], "]"]]]]]]]]], "]"]]]], "+", RowBox[List[FractionBox["245", "128"], " ", "\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["PolyLog", "[", RowBox[List["2", ",", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSin", "[", 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]