html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 AiryBiPrime

 http://functions.wolfram.com/03.08.21.0020.01

 Input Form

 Integrate[Sinh[b + (2/3) (a z)^(3/2)] AiryBiPrime[a z], z] == (E^(-b - (2/3) (a z)^(3/2)) (-6 (1 + E^(2 b + (4/3) (a z)^(3/2))) (a z)^(3/2) (a^(3/2) z^(3/2))^(2/3) AiryBi[a z] Gamma[5/3] + 15 a (-1 + E^(2 b + (4/3) (a z)^(3/2))) z (a^(3/2) z^(3/2))^(2/3) AiryBiPrime[a z] Gamma[5/3] - Sqrt[3] (3 a^3 (-1 + E^(2 b + (4/3) (a z)^(3/2))) z^3 BesselI[-(4/3), (2/3) a^(3/2) z^(3/2)] Gamma[5/3] + (a^(3/2) z^(3/2))^(1/3) (2 3^(1/3) E^((2/3) (a z)^(3/2)) (-1 + E^(2 b)) (a^(3/2) z^(3/2))^(1/3) + 3 a^(5/2) (-1 + E^(2 b + (4/3) (a z)^(3/2))) z^(5/2) BesselI[4/3, (2/3) a^(3/2) z^(3/2)] Gamma[5/3]))))/ (30 a (a^(3/2) z^(3/2))^(2/3) Gamma[5/3])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]], RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], "+", RowBox[List["15", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], "-", RowBox[List[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", SuperscriptBox["z", "3"], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["3", " ", SuperscriptBox["a", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["4", "3"], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["30", " ", "a", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], ")"]]]]]]]]

 MathML Form

 sinh ( 2 3 ( a z ) 3 / 2 + b ) Bi ( a z ) z 1 30 a ( a 3 / 2 z 3 / 2 ) 2 / 3 Γ ( 5 3 ) ( - 1 3 2 ( a z ) 3 / 2 - b ( - 6 ( 1 + 4 3 ( a z ) 3 / 2 + 2 b ) ( a 3 / 2 z 3 / 2 ) 2 / 3 Bi ( a z ) Γ ( 5 3 ) ( a z ) 3 / 2 + 15 a ( - 1 + 4 3 ( a z ) 3 / 2 + 2 b ) z ( a 3 / 2 z 3 / 2 ) 2 / 3 Bi ( a z ) Γ ( 5 3 ) - 3 ( ( 3 a 5 / 2 ( - 1 + 4 3 ( a z ) 3 / 2 + 2 b ) I 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) Γ ( 5 3 ) z 5 / 2 + 2 3 3 2 3 ( a z ) 3 / 2 ( - 1 + 2 b ) a 3 / 2 z 3 / 2 3 ) a 3 / 2 z 3 / 2 3 + 3 a 3 ( - 1 + 4 3 ( a z ) 3 / 2 + 2 b ) z 3 I - 4 3 ( 2 3 a 3 / 2 z 3 / 2 ) Γ ( 5 3 ) ) ) ) z 2 3 a z 3 2 b AiryBiPrime a z 1 30 a a 3 2 z 3 2 2 3 Gamma 5 3 -1 -1 1 3 2 a z 3 2 -1 b -6 1 4 3 a z 3 2 2 b a 3 2 z 3 2 2 3 AiryBi a z Gamma 5 3 a z 3 2 15 a -1 4 3 a z 3 2 2 b z a 3 2 z 3 2 2 3 AiryBiPrime a z Gamma 5 3 -1 3 1 2 3 a 5 2 -1 4 3 a z 3 2 2 b BesselI 4 3 2 3 a 3 2 z 3 2 Gamma 5 3 z 5 2 2 3 1 3 2 3 a z 3 2 -1 2 b a 3 2 z 3 2 1 3 a 3 2 z 3 2 1 3 3 a 3 -1 4 3 a z 3 2 2 b z 3 BesselI -1 4 3 2 3 a 3 2 z 3 2 Gamma 5 3 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sinh", "[", RowBox[List["b_", "+", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a_", " ", "z_"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "b"]], "-", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], "+", RowBox[List["15", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", "z", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["AiryBiPrime", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], "-", RowBox[List[SqrtBox["3"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", SuperscriptBox["z", "3"], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["3", RowBox[List["1", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], "+", RowBox[List["3", " ", SuperscriptBox["a", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["4", "3"], ",", RowBox[List[FractionBox["2", "3"], " ", SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["30", " ", "a", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], ")"]], RowBox[List["2", "/", "3"]]], " ", RowBox[List["Gamma", "[", FractionBox["5", "3"], "]"]]]]]]]]]

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

 2001-10-29