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 CosIntegral

 http://functions.wolfram.com/06.38.21.0045.01

 Input Form

 Integrate[z^(\[Alpha] - 1) Log[b z] CosIntegral[a z], z] == (1/(2 \[Alpha]^3)) ((z^\[Alpha] ((-(I a z)^\[Alpha]) \[Alpha] Gamma[\[Alpha], (-I) a z] - ((-I) a z)^\[Alpha] \[Alpha] Gamma[\[Alpha], I a z] + (a^2 z^2)^\[Alpha] HypergeometricPFQ[{\[Alpha], \[Alpha]}, {1 + \[Alpha], 1 + \[Alpha]}, (-I) a z] + (a^2 z^2)^\[Alpha] HypergeometricPFQ[{\[Alpha], \[Alpha]}, {1 + \[Alpha], 1 + \[Alpha]}, I a z] - ((-I) a z)^\[Alpha] \[Alpha] Gamma[1 + \[Alpha]] Log[z] - (I a z)^\[Alpha] \[Alpha] Gamma[1 + \[Alpha]] Log[z] + (I a z)^\[Alpha] \[Alpha]^2 Gamma[\[Alpha], (-I) a z] Log[b z] + ((-I) a z)^\[Alpha] \[Alpha]^2 Gamma[\[Alpha], I a z] Log[b z] + 2 (a^2 z^2)^\[Alpha] \[Alpha] CosIntegral[a z] (-1 + \[Alpha] Log[b z])))/(a^2 z^2)^\[Alpha])

 Standard Form

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 MathML Form

 z α - 1 log ( b z ) Ci ( a z ) z 1 2 α 3 ( z α ( a 2 z 2 ) - α ( - α Γ ( α , a z ) ( - a z ) α - α Γ ( α + 1 ) log ( z ) ( - a z ) α + α 2 Γ ( α , a z ) log ( b z ) ( - a z ) α - ( a z ) α α Γ ( α , - a z ) + ( a 2 z 2 ) α 2 F 2 ( α , α ; α + 1 , α + 1 ; - a z ) 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["\[Alpha]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Alpha]", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["\[Alpha]", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["\[Alpha]", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + ( a 2 z 2 ) α 2 F 2 ( α , α ; α + 1 , α + 1 ; a z ) 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["\[Alpha]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Alpha]", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["\[Alpha]", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["\[Alpha]", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - ( a z ) α α Γ ( α + 1 ) log ( z ) + ( a z ) α α 2 Γ ( α , - a z ) log ( b z ) + 2 ( a 2 z 2 ) α α Ci ( a z ) ( α log ( b z ) - 1 ) ) ) z z α -1 b z CosIntegral a z 1 2 α 3 -1 z α a 2 z 2 -1 α -1 α Gamma α a z -1 a z α -1 α Gamma α 1 z -1 a z α α 2 Gamma α a z b z -1 a z α -1 a z α α Gamma α -1 a z a 2 z 2 α HypergeometricPFQ α α α 1 α 1 -1 a z a 2 z 2 α HypergeometricPFQ α α α 1 α 1 a z -1 a z α α Gamma α 1 z a z α α 2 Gamma α -1 a z b z 2 a 2 z 2 α α CosIntegral a z α b z -1 [/itex]

 Rule Form

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

 2001-10-29