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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0065.01

 Input Form

 Integrate[z^n ExpIntegralEi[a z] CoshIntegral[a z], z] == (1/(2 (1 + n))) (2 CoshIntegral[a z] (z^(1 + n) ExpIntegralEi[a z] + (-a)^(-1 - n) Gamma[1 + n, (-a) z]) + (n! (ExpIntegralEi[2 a z] + Log[z]))/((-a)^n a) - a^(-1 - n) (ExpIntegralEi[a z] ((-1)^n Gamma[1 + n, (-a) z] - Gamma[1 + n, a z]) + n! ((-(-1)^n) ExpIntegralEi[2 a z] + Log[z]) - (1/(1 + n)^2) (a z (a z)^n HypergeometricPFQ[{1, 1 + n}, {2 + n, 2 + n}, a z] + (1 + n)^2 n! (EulerGamma + Gamma[0, (-a) z] + Log[(-a) z])) + (-1)^n n! Sum[Gamma[k, -2 a z]/(2^k k!), {k, 1, n}]) + ((2 n!)/((-a)^n a)) Sum[(((-a) z)^k/(2 k) - 2^(-1 - k) Gamma[k, -2 a z])/ k!, {k, 1, n}]) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n Ei ( a z ) Chi ( a z ) z 1 2 ( n + 1 ) ( - a - n - 1 ( Ei ( a z ) ( ( - 1 ) n Γ ( n + 1 , - a z ) - Γ ( n + 1 , a z ) ) + n ! ( log ( z ) - ( - 1 ) n Ei ( 2 a z ) ) - 1 ( n + 1 ) 2 ( a z 2 F 2 ( 1 , n + 1 ; n + 2 , n + 2 ; 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["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["n", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["n", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["n", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["a", " ", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ( a z ) n + ( n + 1 ) 2 n ! ( Γ ( 0 , - a z ) + log ( - a z ) + TagBox["\[DoubledGamma]", Function[EulerGamma]] ) ) + ( - 1 ) n n ! k = 1 n 2 - k Γ ( k , - 2 a z ) k ! ) + 2 Chi ( a z ) ( Γ ( n + 1 , - a z ) ( - a ) - n - 1 + z n + 1 Ei ( a z ) ) + 2 ( - a ) - n n ! a k = 1 n 1 k ! ( ( - a z ) k 2 k - 2 - k - 1 Γ ( k , - 2 a z ) ) + ( - a ) - n n ! ( Ei ( 2 a z ) + log ( z ) ) a ) /; n Condition z z n ExpIntegralEi a z CoshIntegral a z 1 2 n 1 -1 -1 a -1 n -1 ExpIntegralEi a z -1 n Gamma n 1 -1 a z -1 Gamma n 1 a z n z -1 -1 n ExpIntegralEi 2 a z -1 1 n 1 2 -1 a z HypergeometricPFQ 1 n 1 n 2 n 2 a z a z n n 1 2 n Gamma 0 -1 a z -1 a z -1 n n k 1 n 2 -1 k Gamma k -2 a z k -1 2 CoshIntegral a z Gamma n 1 -1 a z -1 a -1 n -1 z n 1 ExpIntegralEi a z 2 -1 a -1 n n a -1 k 1 n 1 k -1 -1 a z k 2 k -1 -1 2 -1 k -1 Gamma k -2 a z -1 a -1 n n ExpIntegralEi 2 a z z a -1 n [/itex]

 Rule Form

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

 2001-10-29