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 HypergeometricPFQ

 Input Form

 HypergeometricPFQ[{-(5/2), 3, 3}, {5/2, 5/2}, z] == -((1/(4194304 z^(3/2))) (I (-5760 Pi^2 - 70080 I Sqrt[z] - 103680 Pi^2 z + 2701024 I z^(3/2) + 972000 Pi^2 z^2 - 6262200 I z^(5/2) - 1764000 Pi^2 z^3 + 3572100 I z^(7/2) + 893025 Pi^2 z^4))) + (15 Sqrt[1 - z] (784 + 18152 z - 77910 z^2 + 59535 z^3) ArcSin[Sqrt[z]])/ (1048576 z^(3/2)) - (1/(9437184 (-1 + z)^8 z)) (Sqrt[1 - z] (-51840 + 15693824 z - 268696608 z^2 + 1284314016 z^3 - 3811268215 z^4 + 7322146190 z^5 - 9571486384 z^6 + 8632630418 z^7 - 5309470691 z^8 + 2132820250 z^9 - 505590750 z^10 + 53734590 z^11) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(9437184 (-1 + z)^8 z)) (Sqrt[1 - z] (-51840 + 15693824 z - 268696608 z^2 + 1284314016 z^3 - 3811268215 z^4 + 7322146190 z^5 - 9571486384 z^6 + 8632630418 z^7 - 5309470691 z^8 + 2132820250 z^9 - 505590750 z^10 + 53734590 z^11) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) - (1/(1048576 z^(3/2))) (45 (-128 - 2304 z + 21600 z^2 - 39200 z^3 + 19845 z^4) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))]) + (1/(9437184 (-1 + z)^8 z)) (Sqrt[1 - z] (-51840 + 15693824 z - 268696608 z^2 + 1284314016 z^3 - 3811268215 z^4 + 7322146190 z^5 - 9571486384 z^6 + 8632630418 z^7 - 5309470691 z^8 + 2132820250 z^9 - 505590750 z^10 + 53734590 z^11) Log[1 + E^(I ArcSin[Sqrt[z]])]) - (45 I (-128 - 2304 z + 21600 z^2 - 39200 z^3 + 19845 z^4) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/(1048576 z^(3/2)) + (45 I (-128 - 2304 z + 21600 z^2 - 39200 z^3 + 19845 z^4) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(1048576 z^(3/2))

 Standard Form

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 MathML Form

 3 F 2 ( - 5 2 , 3 , 3 ; 5 2 , 5 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 1 4194304 z 3 / 2 ( ( 893025 π 2 z 4 + 3572100 z 7 / 2 - 1764000 π 2 z 3 - 6262200 z 5 / 2 + 972000 π 2 z 2 + 2701024 z 3 / 2 - 103680 π 2 z - 70080 z - 5760 π 2 ) ) + 15 1 - z ( 59535 z 3 - 77910 z 2 + 18152 z + 784 ) sin - 1 ( z ) 1048576 z 3 / 2 - 1 9437184 ( z - 1 ) 8 z ( 1 - z ( 53734590 z 11 - 505590750 z 10 + 2132820250 z 9 - 5309470691 z 8 + 8632630418 z 7 - 9571486384 z 6 + 7322146190 z 5 - 3811268215 z 4 + 1284314016 z 3 - 268696608 z 2 + 15693824 z - 51840 ) log ( 1 - sin - 1 ( z ) ) ) + 1 9437184 ( z - 1 ) 8 z ( 1 - z ( 53734590 z 11 - 505590750 z 10 + 2132820250 z 9 - 5309470691 z 8 + 8632630418 z 7 - 9571486384 z 6 + 7322146190 z 5 - 3811268215 z 4 + 1284314016 z 3 - 268696608 z 2 + 15693824 z - 51840 ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) ) - 45 ( 19845 z 4 - 39200 z 3 + 21600 z 2 - 2304 z - 128 ) sin - 1 ( z ) log ( 1 - sin - 1 ( z ) 1 + sin - 1 ( z ) ) 1048576 z 3 / 2 + 1 9437184 ( z - 1 ) 8 z ( 1 - z ( 53734590 z 11 - 505590750 z 10 + 2132820250 z 9 - 5309470691 z 8 + 8632630418 z 7 - 9571486384 z 6 + 7322146190 z 5 - 3811268215 z 4 + 1284314016 z 3 - 268696608 z 2 + 15693824 z - 51840 ) log ( 1 + sin - 1 ( z ) ) ) - 45 ( 19845 z 4 - 39200 z 3 + 21600 z 2 - 2304 z - 128 ) Li PolyLog 2 ( - sin - 1 ( z ) ) 1048576 z 3 / 2 + 45 ( 19845 z 4 - 39200 z 3 + 21600 z 2 - 2304 z - 128 ) Li PolyLog 2 ( sin - 1 ( z ) ) 1048576 z 3 / 2 HypergeometricPFQ -1 5 2 3 3 5 2 5 2 z -1 1 4194304 z 3 2 -1 893025 2 z 4 3572100 z 7 2 -1 1764000 2 z 3 -1 6262200 z 5 2 972000 2 z 2 2701024 z 3 2 -1 103680 2 z -1 70080 z 1 2 -1 5760 2 15 1 -1 z 1 2 59535 z 3 -1 77910 z 2 18152 z 784 z 1 2 1048576 z 3 2 -1 -1 1 9437184 z -1 8 z -1 1 -1 z 1 2 53734590 z 11 -1 505590750 z 10 2132820250 z 9 -1 5309470691 z 8 8632630418 z 7 -1 9571486384 z 6 7322146190 z 5 -1 3811268215 z 4 1284314016 z 3 -1 268696608 z 2 15693824 z -51840 1 -1 z 1 2 1 9437184 z -1 8 z -1 1 -1 z 1 2 53734590 z 11 -1 505590750 z 10 2132820250 z 9 -1 5309470691 z 8 8632630418 z 7 -1 9571486384 z 6 7322146190 z 5 -1 3811268215 z 4 1284314016 z 3 -1 268696608 z 2 15693824 z -51840 1 -1 z 1 2 1 z 1 2 -1 -1 45 19845 z 4 -1 39200 z 3 21600 z 2 -1 2304 z -128 z 1 2 1 -1 z 1 2 1 z 1 2 -1 1048576 z 3 2 -1 1 9437184 z -1 8 z -1 1 -1 z 1 2 53734590 z 11 -1 505590750 z 10 2132820250 z 9 -1 5309470691 z 8 8632630418 z 7 -1 9571486384 z 6 7322146190 z 5 -1 3811268215 z 4 1284314016 z 3 -1 268696608 z 2 15693824 z -51840 1 z 1 2 -1 45 19845 z 4 -1 39200 z 3 21600 z 2 -1 2304 z -128 PolyLog 2 -1 z 1 2 1048576 z 3 2 -1 45 19845 z 4 -1 39200 z 3 21600 z 2 -1 2304 z -128 PolyLog 2 z 1 2 1048576 z 3 2 -1 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02