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 AiryBi

 http://functions.wolfram.com/03.06.21.0022.01

 Input Form

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

 Standard Form

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 MathML Form

 sinh ( 2 3 ( a z r ) 3 / 2 ) Bi ( a z r ) z - 1 2 3 5 / 6 ( r + 1 ) Γ ( 2 3 ) Γ ( 4 3 ) ( z ( a Γ ( 2 3 ) ( 2 F 2 ( 5 6 , 2 3 + 2 3 r ; 5 3 , 5 3 + 2 3 r ; 1 3 ( - 4 ) ( a z r ) 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[RowBox[List[FractionBox["2", "3"], "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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[RowBox[List[FractionBox["5", "3"], "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 2 F 2 ( 5 6 , 2 3 + 2 3 r ; 5 3 , 5 3 + 2 3 r ; 4 3 ( a z r ) 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[RowBox[List[FractionBox["2", "3"], "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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[RowBox[List[FractionBox["5", "3"], "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) z r - 3 2 / 3 ( r + 1 ) Γ ( 4 3 ) 2 F 2 ( 1 6 , 2 3 r ; 1 3 , 1 + 2 3 r ; 4 3 ( a z r ) 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", RowBox[List["3", " ", "r"]]], 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[RowBox[List["1", "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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", " ", SuperscriptBox["z", "r"]]], ")"]], RowBox[List["3", "/", "2"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + 3 2 / 3 ( r + 1 ) Γ ( 4 3 ) 2 F 2 ( 1 6 , 2 3 r ; 1 3 , 1 + 2 3 r ; 1 3 ( - 4 ) ( a z r ) 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", RowBox[List["3", " ", "r"]]], 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[RowBox[List["1", "+", FractionBox["2", RowBox[List["3", " ", "r"]]]]], 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", " ", SuperscriptBox["z", "r"]]], ")"]], 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 r 3 2 AiryBi a z r -1 1 2 3 5 6 r 1 Gamma 2 3 Gamma 4 3 -1 z a Gamma 2 3 HypergeometricPFQ 5 6 2 3 2 3 r -1 5 3 5 3 2 3 r -1 1 3 -4 a z r 3 2 -1 HypergeometricPFQ 5 6 2 3 2 3 r -1 5 3 5 3 2 3 r -1 4 3 a z r 3 2 z r -1 3 2 3 r 1 Gamma 4 3 HypergeometricPFQ 1 6 2 3 r -1 1 3 1 2 3 r -1 4 3 a z r 3 2 3 2 3 r 1 Gamma 4 3 HypergeometricPFQ 1 6 2 3 r -1 1 3 1 2 3 r -1 1 3 -4 a z r 3 2 [/itex]

 Rule Form

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

 2001-10-29