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 AiryBi

 http://functions.wolfram.com/03.06.21.0021.01

 Input Form

 Integrate[Sinh[b + (2/3) (a z)^(3/2)] AiryBi[a z], z] == (z (-2 3^(2/3) Gamma[4/3] HypergeometricPFQ[{1/6, 2/3}, {1/3, 5/3}, (-(4/3)) (a z)^(3/2)] + 2 3^(2/3) E^(2 b) Gamma[4/3] HypergeometricPFQ[{1/6, 2/3}, {1/3, 5/3}, (4/3) (a z)^(3/2)] - a z Gamma[2/3] (HypergeometricPFQ[{5/6, 4/3}, {5/3, 7/3}, (-(4/3)) (a z)^(3/2)] - E^(2 b) HypergeometricPFQ[{5/6, 4/3}, {5/3, 7/3}, (4/3) (a z)^(3/2)])))/E^b/ (4 3^(5/6) Gamma[2/3] Gamma[4/3])

 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["AiryBi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "b"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", RowBox[List["Gamma", "[", FractionBox["4", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", FractionBox["5", "3"]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]], "+", RowBox[List["2", " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b"]]], " ", RowBox[List["Gamma", "[", FractionBox["4", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", FractionBox["5", "3"]]], "}"]], ",", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]], "-", RowBox[List["a", " ", "z", " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", FractionBox["4", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "3"], ",", FractionBox["7", "3"]]], "}"]], ",", RowBox[List[RowBox[List["-", FractionBox["4", "3"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", FractionBox["4", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "3"], ",", FractionBox["7", "3"]]], "}"]], ",", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["4", "3"], "]"]]]], ")"]]]]]]]]

 MathML Form

 sinh ( 2 3 ( a z ) 3 / 2 + b ) Bi ( a z ) z 1 4 3 5 / 6 Γ ( 2 3 ) Γ ( 4 3 ) ( - b z ( 2 3 2 / 3 2 b Γ ( 4 3 ) 2 F 2 ( 1 6 , 2 3 ; 1 3 , 5 3 ; 4 3 ( a z ) 3 / 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["1", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["2", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 2 3 2 / 3 Γ ( 4 3 ) 2 F 2 ( 1 6 , 2 3 ; 1 3 , 5 3 ; 1 3 ( - 4 ) ( a z ) 3 / 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["1", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["2", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - a z Γ ( 2 3 ) ( 2 F 2 ( 5 6 , 4 3 ; 5 3 , 7 3 ; 1 3 ( - 4 ) ( a z ) 3 / 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", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["4", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 2 b 2 F 2 ( 5 6 , 4 3 ; 5 3 , 7 3 ; 4 3 ( a z ) 3 / 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", "6"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["4", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) ) ) z 2 3 a z 3 2 b AiryBi a z 1 4 3 5 6 Gamma 2 3 Gamma 4 3 -1 -1 b z 2 3 2 3 2 b Gamma 4 3 HypergeometricPFQ 1 6 2 3 1 3 5 3 4 3 a z 3 2 -1 2 3 2 3 Gamma 4 3 HypergeometricPFQ 1 6 2 3 1 3 5 3 1 3 -4 a z 3 2 -1 a z Gamma 2 3 HypergeometricPFQ 5 6 4 3 5 3 7 3 1 3 -4 a z 3 2 -1 2 b HypergeometricPFQ 5 6 4 3 5 3 7 3 4 3 a z 3 2 [/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["AiryBi", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "b"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", RowBox[List["Gamma", "[", FractionBox["4", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", FractionBox["5", "3"]]], "}"]], ",", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]], "+", RowBox[List["2", " ", SuperscriptBox["3", RowBox[List["2", "/", "3"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b"]]], " ", RowBox[List["Gamma", "[", FractionBox["4", "3"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "6"], ",", FractionBox["2", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "3"], ",", FractionBox["5", "3"]]], "}"]], ",", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]], "-", RowBox[List["a", " ", "z", " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", FractionBox["4", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "3"], ",", FractionBox["7", "3"]]], "}"]], ",", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["-", "4"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "6"], ",", FractionBox["4", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "3"], ",", FractionBox["7", "3"]]], "}"]], ",", RowBox[List[FractionBox["4", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["4", " ", SuperscriptBox["3", RowBox[List["5", "/", "6"]]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]], " ", RowBox[List["Gamma", "[", FractionBox["4", "3"], "]"]]]]]]]]]

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

 2001-10-29