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 FresnelC

 http://functions.wolfram.com/06.33.21.0107.01

 Input Form

 Integrate[z^3 Log[b z] Erf[a z], z] == ((1/(1600 a^5 Pi^2 z)) (8 a^6 E^((1/2) I a^2 Pi z^2) Pi^2 z^6 (HypergeometricPFQ[{5/2, 5/2}, {7/2, 7/2}, (-(1/2)) I a^2 Pi z^2] + HypergeometricPFQ[{5/2, 5/2}, {7/2, 7/2}, (1/2) I a^2 Pi z^2]) + 25 (2 I a^2 z^2 (3 I - a^2 Pi z^2 + E^(I a^2 Pi z^2) (3 I + a^2 Pi z^2)) (-1 + 4 Log[b z]) + 3 I Sqrt[2] E^((1/2) I a^2 Pi z^2) (Sqrt[(-I) a^2 z^2] - Sqrt[I a^2 z^2]) (1 + 4 Log[z] - 4 Log[b z]) + 4 a E^((1/2) I a^2 Pi z^2) z (3 + a^4 Pi^2 z^4) FresnelC[a z] (-1 + 4 Log[b z]))))/E^((1/2) I a^2 Pi z^2)

 Standard Form

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 MathML Form

 z 3 log ( b z ) erf ( a z ) z 1 1600 a 5 π 2 z - 1 2 a 2 π z 2 ( 8 a 6 1 2 a 2 π z 2 π 2 ( 2 F 2 ( 5 2 , 5 2 ; 7 2 , 7 2 ; 1 2 a 2 π z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", SuperscriptBox["a", "2"], " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + 2 F 2 ( 5 2 , 5 2 ; 7 2 , 7 2 ; - 1 2 a 2 π z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", SuperscriptBox["a", "2"], " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) z 6 + 25 ( 2 a 2 ( - a 2 π z 2 + 3 + a 2 π z 2 ( a 2 π z 2 + 3 ) ) ( 4 log ( b z ) - 1 ) z 2 + 4 a 1 2 a 2 π z 2 ( a 4 π 2 z 4 + 3 ) C TagBox["C", FresnelC] ( a z ) ( 4 log ( b z ) - 1 ) z + 3 2 1 2 a 2 π z 2 ( - a 2 z 2 - a 2 z 2 ) ( 4 log ( z ) - 4 log ( b z ) + 1 ) ) ) z z 3 b z Erf a z 1 1600 a 5 2 z -1 -1 1 2 a 2 z 2 8 a 6 1 2 a 2 z 2 2 HypergeometricPFQ 5 2 5 2 7 2 7 2 1 2 a 2 z 2 HypergeometricPFQ 5 2 5 2 7 2 7 2 -1 1 2 a 2 z 2 z 6 25 2 a 2 -1 a 2 z 2 3 a 2 z 2 a 2 z 2 3 4 b z -1 z 2 4 a 1 2 a 2 z 2 a 4 2 z 4 3 FresnelC a z 4 b z -1 z 3 2 1 2 1 2 a 2 z 2 -1 a 2 z 2 1 2 -1 a 2 z 2 1 2 4 z -1 4 b z 1 [/itex]

 Rule Form

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

 2001-10-29