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 StruveH

 http://functions.wolfram.com/03.09.06.0055.01

 Input Form

 StruveH[\[Nu], z] \[Proportional] ((-1)^(1 + \[Nu])/Sqrt[-2 Pi z]) (Exp[(-I) z - ((2 \[Nu] + 3)/4) Pi I] HypergeometricPFQ[ {1/2 + \[Nu], 1/2 - \[Nu]}, {}, I/(2 z)] + Exp[I z + ((2 \[Nu] + 3)/4) Pi I] HypergeometricPFQ[ {1/2 + \[Nu], 1/2 - \[Nu]}, {}, -(I/(2 z))]) + ((2^(1 - \[Nu]) (-1)^(1 + \[Nu]) (-z)^(\[Nu] - 1))/ (Sqrt[Pi] Gamma[1/2 + \[Nu]])) HypergeometricPFQ[{1/2, 1/2 - \[Nu], 1}, {}, -(4/z^2)] /; Inequality[0, Less, Arg[z], LessEqual, Pi] && (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StruveH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], " "]], SqrtBox[RowBox[List[RowBox[List["-", "2"]], "\[Pi]", " ", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "-", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "\[Nu]"]], "+", "3"]], "4"], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["\[ImaginaryI]", RowBox[List["2", " ", "z"]]]]], "]"]]]], "+", RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "\[Nu]"]], "+", "3"]], "4"], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["-", FractionBox["\[ImaginaryI]", RowBox[List["2", " ", "z"]]]]]]], "]"]]]]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]]]], RowBox[List[SqrtBox["\[Pi]"], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ",", "1"]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["-", FractionBox["4", SuperscriptBox["z", "2"]]]]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

 MathML Form

 H StruveH ν ( z ) ( - 1 ) ν + 1 - 2 π z ( - z - 2 ν + 3 4 π 2 F 0 ( ν + 1 2 , 1 2 - ν ; ; 2 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["0", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["\[ImaginaryI]", RowBox[List["2", " ", "z"]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + z + 2 ν + 3 4 π 2 F 0 ( ν + 1 2 , 1 2 - ν ; ; - 2 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["0", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["\[ImaginaryI]", RowBox[List["2", " ", "z"]]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) + 2 1 - ν ( - 1 ) ν + 1 ( - z ) ν - 1 π Γ ( ν + 1 2 ) 3 F 0 ( 1 2 , 1 2 - ν , 1 ; ; - 4 z 2 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["0", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["4", SuperscriptBox["z", "2"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] /; 0 < arg ( z ) π ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional StruveH ν z -1 ν 1 -2 z 1 2 -1 -1 z -1 2 ν 3 4 -1 HypergeometricPFQ ν 1 2 1 2 -1 ν 2 z -1 z 2 ν 3 4 -1 HypergeometricPFQ ν 1 2 1 2 -1 ν -1 2 z -1 2 1 -1 ν -1 ν 1 -1 z ν -1 1 2 Gamma ν 1 2 -1 HypergeometricPFQ 1 2 1 2 -1 ν 1 -1 4 z 2 -1 Inequality 0 z Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveH", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "-", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", FractionBox["\[ImaginaryI]", RowBox[List["2", " ", "z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["-", FractionBox["\[ImaginaryI]", RowBox[List["2", " ", "z"]]]]]]], "]"]]]]]], ")"]]]], SqrtBox[RowBox[List[RowBox[List["-", "2"]], " ", "\[Pi]", " ", "z"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ",", "1"]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["-", FractionBox["4", SuperscriptBox["z", "2"]]]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]]]

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

 2007-05-02