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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0066.01

 Input Form

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

 Rule Form

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

 2001-10-29