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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.9261.01

 Input Form

 HypergeometricPFQ[{-(7/2), 3, 3}, {-(1/2), 7/2}, -z] == (1/(2097152 z^2)) (-161280 - 26880 z + 1791616 z^2 - 32655168 z^3 - 15435000 Pi^2 z^(7/2) - 168021000 z^4 - 50009400 Pi^2 z^(9/2) - 144074700 z^5 - 36018675 Pi^2 z^(11/2)) + (1/(25165824 (1 + z)^(21/2))) ((61093888 + 11466040320 z - 95930144128 z^2 + 846414579136 z^3 + 2263375024176 z^4 + 7720853120008 z^5 + 16686834369380 z^6 + 26200923536832 z^7 + 30321038787431 z^8 + 25962480465551 z^9 + 16288146892080 z^10 + 7291345027050 z^11 + 2208527968395 z^12 + 406144654335 z^13 + 34276868010 z^14) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(25165824 (1 + z)^(21/2))) ((-61093888 - 11466040320 z + 95930144128 z^2 - 846414579136 z^3 - 2263375024176 z^4 - 7720853120008 z^5 - 16686834369380 z^6 - 26200923536832 z^7 - 30321038787431 z^8 - 25962480465551 z^9 - 16288146892080 z^10 - 7291345027050 z^11 - 2208527968395 z^12 - 406144654335 z^13 - 34276868010 z^14) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (1/(524288 z^(5/2))) (105 Sqrt[1 + z] (-384 + 64 z - 800 z^2 + 12432 z^3 + 247590 z^4 + 343035 z^5) Log[Sqrt[z] + Sqrt[1 + z]]) + (1/(25165824 (1 + z)^(21/2))) ((-61093888 - 11466040320 z + 95930144128 z^2 - 846414579136 z^3 - 2263375024176 z^4 - 7720853120008 z^5 - 16686834369380 z^6 - 26200923536832 z^7 - 30321038787431 z^8 - 25962480465551 z^9 - 16288146892080 z^10 - 7291345027050 z^11 - 2208527968395 z^12 - 406144654335 z^13 - 34276868010 z^14) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) - (11025 z^(3/2) (1400 + 4536 z + 3267 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/524288 - (11025 z^(3/2) (1400 + 4536 z + 3267 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/524288 + (11025 z^(3/2) (1400 + 4536 z + 3267 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/524288

 Standard Form

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 MathML Form

 3 F 2 ( - 7 2 , 3 , 3 ; - 1 2 , 7 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["7", "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[RowBox[List["-", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 11025 ( 3267 z 2 + 4536 z + 1400 ) log ( z + z + 1 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) z 3 / 2 524288 - 11025 ( 3267 z 2 + 4536 z + 1400 ) Li PolyLog 2 ( - 1 z + z + 1 ) z 3 / 2 524288 + 11025 ( 3267 z 2 + 4536 z + 1400 ) Li PolyLog 2 ( 1 z + z + 1 ) z 3 / 2 524288 + 1 25165824 ( z + 1 ) 21 / 2 ( ( 34276868010 z 14 + 406144654335 z 13 + 2208527968395 z 12 + 7291345027050 z 11 + 16288146892080 z 10 + 25962480465551 z 9 + 30321038787431 z 8 + 26200923536832 z 7 + 16686834369380 z 6 + 7720853120008 z 5 + 2263375024176 z 4 + 846414579136 z 3 - 95930144128 z 2 + 11466040320 z + 61093888 ) log ( z - z + 1 + 1 ) ) + 1 25165824 ( z + 1 ) 21 / 2 ( ( - 34276868010 z 14 - 406144654335 z 13 - 2208527968395 z 12 - 7291345027050 z 11 - 16288146892080 z 10 - 25962480465551 z 9 - 30321038787431 z 8 - 26200923536832 z 7 - 16686834369380 z 6 - 7720853120008 z 5 - 2263375024176 z 4 - 846414579136 z 3 + 95930144128 z 2 - 11466040320 z - 61093888 ) log ( - z + z + 1 + 1 ) ) + 1 25165824 ( z + 1 ) 21 / 2 ( ( - 34276868010 z 14 - 406144654335 z 13 - 2208527968395 z 12 - 7291345027050 z 11 - 16288146892080 z 10 - 25962480465551 z 9 - 30321038787431 z 8 - 26200923536832 z 7 - 16686834369380 z 6 - 7720853120008 z 5 - 2263375024176 z 4 - 846414579136 z 3 + 95930144128 z 2 - 11466040320 z - 61093888 ) log ( z + z + 1 - 1 z + z + 1 + 1 ) ) + 1 2097152 z 2 ( - 36018675 π 2 z 11 / 2 - 144074700 z 5 - 50009400 π 2 z 9 / 2 - 168021000 z 4 - 15435000 π 2 z 7 / 2 - 32655168 z 3 + 1791616 z 2 - 26880 z - 161280 ) - 105 z + 1 ( 343035 z 5 + 247590 z 4 + 12432 z 3 - 800 z 2 + 64 z - 384 ) log ( z + z + 1 ) 524288 z 5 / 2 HypergeometricPFQ -1 7 2 3 3 -1 1 2 7 2 -1 z -1 11025 3267 z 2 4536 z 1400 z 1 2 z 1 1 2 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 z 3 2 524288 -1 -1 11025 3267 z 2 4536 z 1400 PolyLog 2 -1 1 z 1 2 z 1 1 2 -1 z 3 2 524288 -1 11025 3267 z 2 4536 z 1400 PolyLog 2 1 z 1 2 z 1 1 2 -1 z 3 2 524288 -1 1 25165824 z 1 21 2 -1 34276868010 z 14 406144654335 z 13 2208527968395 z 12 7291345027050 z 11 16288146892080 z 10 25962480465551 z 9 30321038787431 z 8 26200923536832 z 7 16686834369380 z 6 7720853120008 z 5 2263375024176 z 4 846414579136 z 3 -1 95930144128 z 2 11466040320 z 61093888 z 1 2 -1 z 1 1 2 1 1 25165824 z 1 21 2 -1 -34276868010 z 14 -1 406144654335 z 13 -1 2208527968395 z 12 -1 7291345027050 z 11 -1 16288146892080 z 10 -1 25962480465551 z 9 -1 30321038787431 z 8 -1 26200923536832 z 7 -1 16686834369380 z 6 -1 7720853120008 z 5 -1 2263375024176 z 4 -1 846414579136 z 3 95930144128 z 2 -1 11466040320 z -61093888 -1 z 1 2 z 1 1 2 1 1 25165824 z 1 21 2 -1 -34276868010 z 14 -1 406144654335 z 13 -1 2208527968395 z 12 -1 7291345027050 z 11 -1 16288146892080 z 10 -1 25962480465551 z 9 -1 30321038787431 z 8 -1 26200923536832 z 7 -1 16686834369380 z 6 -1 7720853120008 z 5 -1 2263375024176 z 4 -1 846414579136 z 3 95930144128 z 2 -1 11466040320 z -61093888 z 1 2 z 1 1 2 -1 z 1 2 z 1 1 2 1 -1 1 2097152 z 2 -1 -36018675 2 z 11 2 -1 144074700 z 5 -1 50009400 2 z 9 2 -1 168021000 z 4 -1 15435000 2 z 7 2 -1 32655168 z 3 1791616 z 2 -1 26880 z -161280 -1 105 z 1 1 2 343035 z 5 247590 z 4 12432 z 3 -1 800 z 2 64 z -384 z 1 2 z 1 1 2 524288 z 5 2 -1 [/itex]

 Rule Form

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

 2007-05-02