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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c53t.01

 Input Form

 Hypergeometric2F1[15/8, 2, 39/8, -z] == (1/(57344 z^(31/8))) (713 (-1)^(1/8) (2760 (-1)^(7/8) z^(7/8) + 2312 (-1)^(7/8) z^(15/8) + 105 (23 + 30 z + 7 z^2) Log[1 - (-1)^(1/8) z^(1/8)] - 105 (23 + 30 z + 7 z^2) Log[1 + (-1)^(1/8) z^(1/8)] + 2415 (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] + 3150 (-1)^(1/4) z Log[1 - (-1)^(3/8) z^(1/8)] + 735 (-1)^(1/4) z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 2415 (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] - 3150 (-1)^(1/4) z Log[1 + (-1)^(3/8) z^(1/8)] - 735 (-1)^(1/4) z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 2415 I Log[1 - (-1)^(5/8) z^(1/8)] + 3150 I z Log[1 - (-1)^(5/8) z^(1/8)] + 735 I z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 2415 I Log[1 + (-1)^(5/8) z^(1/8)] - 3150 I z Log[1 + (-1)^(5/8) z^(1/8)] - 735 I z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 2415 (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] + 3150 (-1)^(3/4) z Log[1 - (-1)^(7/8) z^(1/8)] + 735 (-1)^(3/4) z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 2415 (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)] - 3150 (-1)^(3/4) z Log[1 + (-1)^(7/8) z^(1/8)] - 735 (-1)^(3/4) z^2 Log[1 + (-1)^(7/8) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 15 8 , 2 ; 39 8 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["15", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["39", "8"], 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] 1 57344 z 31 / 8 ( 713 - 1 8 ( 735 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 735 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 735 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 735 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 735 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 735 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 2312 ( - 1 ) 7 / 8 z 15 / 8 + 3150 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z - 3150 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z + 3150 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z - 3150 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 3150 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 3150 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 2760 ( - 1 ) 7 / 8 z 7 / 8 + 105 ( 7 z 2 + 30 z + 23 ) log ( 1 - - 1 8 z 8 ) - 105 ( 7 z 2 + 30 z + 23 ) log ( - 1 8 z 8 + 1 ) + 2415 - 1 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 2415 - 1 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 2415 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 2415 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 2415 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 2415 ( - 1 ) 3 / 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 15 8 2 39 8 -1 z 1 57344 z 31 8 -1 713 -1 1 8 735 -1 1 4 1 -1 -1 3 8 z 1 8 z 2 -1 735 -1 1 4 -1 3 8 z 1 8 1 z 2 735 1 -1 -1 5 8 z 1 8 z 2 -1 735 -1 5 8 z 1 8 1 z 2 735 -1 3 4 1 -1 -1 7 8 z 1 8 z 2 -1 735 -1 3 4 -1 7 8 z 1 8 1 z 2 2312 -1 7 8 z 15 8 3150 -1 1 4 1 -1 -1 3 8 z 1 8 z -1 3150 -1 1 4 -1 3 8 z 1 8 1 z 3150 1 -1 -1 5 8 z 1 8 z -1 3150 -1 5 8 z 1 8 1 z 3150 -1 3 4 1 -1 -1 7 8 z 1 8 z -1 3150 -1 3 4 -1 7 8 z 1 8 1 z 2760 -1 7 8 z 7 8 105 7 z 2 30 z 23 1 -1 -1 1 8 z 1 8 -1 105 7 z 2 30 z 23 -1 1 8 z 1 8 1 2415 -1 1 4 1 -1 -1 3 8 z 1 8 -1 2415 -1 1 4 -1 3 8 z 1 8 1 2415 1 -1 -1 5 8 z 1 8 -1 2415 -1 5 8 z 1 8 1 2415 -1 3 4 1 -1 -1 7 8 z 1 8 -1 2415 -1 3 4 -1 7 8 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02