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 | | http://functions.wolfram.com/07.17.26.0093.01 | 
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 | | Sin[z] Hypergeometric0F1[b, -(z^2/4)] == (1/z) 2^(b - 3/2) Gamma[b] 
  MeijerG[{{5/4 - b/2, 7/4 - b/2}, {}}, {{1}, {1/2, 3/2 - b, 2 - b}}, z^2] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sin", "[", "z", "]"]], RowBox[List["Hypergeometric0F1", "[", RowBox[List["b", ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "z"], SuperscriptBox["2", RowBox[List["b", "-", FractionBox["3", "2"]]]], RowBox[List["Gamma", "[", "b", "]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["5", "4"], "-", FractionBox["b", "2"]]], ",", RowBox[List[FractionBox["7", "4"], "-", FractionBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["3", "2"], "-", "b"]], ",", RowBox[List["2", "-", "b"]]]], "}"]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]]]]]] | 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <mrow>  <mi> sin </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 0 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mo>   </mo>  <mo> ; </mo>  <mi> b </mi>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mn> 4 </mn>  </mfrac>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["b", Hypergeometric0F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], Hypergeometric0F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1] </annotation>  </semantics>  </mrow>  <mo>  </mo>  <mrow>  <mfrac>  <mrow>  <msup>  <mn> 2 </mn>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> b </mi>  <mo> ) </mo>  </mrow>  <mtext>   </mtext>  </mrow>  <mi> z </mi>  </mfrac>  <mo> ⁢ </mo>  <semantics>  <mrow>  <msubsup>  <mi> G </mi>  <mrow>  <mn> 2 </mn>  <mo> , </mo>  <mn> 4 </mn>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mn> 2 </mn>  </mrow>  </msubsup>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mo> ❘ </mo>  <mtable>  <mtr>  <mtd>  <mrow>  <mrow>  <mfrac>  <mn> 5 </mn>  <mn> 4 </mn>  </mfrac>  <mo> - </mo>  <mfrac>  <mi> b </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mfrac>  <mn> 7 </mn>  <mn> 4 </mn>  </mfrac>  <mo> - </mo>  <mfrac>  <mi> b </mi>  <mn> 2 </mn>  </mfrac>  </mrow>  </mrow>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mrow>  <mfrac>  <mn> 3 </mn>  <mn> 2 </mn>  </mfrac>  <mo> - </mo>  <mi> b </mi>  </mrow>  <mo> , </mo>  <mrow>  <mn> 2 </mn>  <mo> - </mo>  <mi> b </mi>  </mrow>  </mrow>  </mtd>  </mtr>  </mtable>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["1", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[SuperscriptBox["z", "2"], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[FractionBox["5", "4"], "-", FractionBox["b", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["7", "4"], "-", FractionBox["b", "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["1", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", "b"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["2", "-", "b"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation>  </semantics>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <times />  <apply>  <sin />  <ci> z </ci>  </apply>  <apply>  <ci> Hypergeometric0F1 </ci>  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 4 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <apply>  <power />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <ci> b </ci>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> MeijerG </ci>  <list>  <list>  <apply>  <plus />  <cn type='rational'> 5 <sep /> 4 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> b </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <cn type='rational'> 7 <sep /> 4 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> b </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </list>  <list />  </list>  <list>  <list>  <cn type='integer'> 1 </cn>  </list>  <list>  <cn type='rational'> 1 <sep /> 2 </cn>  <apply>  <plus />  <cn type='rational'> 3 <sep /> 2 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 2 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  </apply>  </list>  </list>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Sin", "[", "z_", "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List["b_", ",", RowBox[List["-", FractionBox[SuperscriptBox["z_", "2"], "4"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["b", "-", FractionBox["3", "2"]]]], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["5", "4"], "-", FractionBox["b", "2"]]], ",", RowBox[List[FractionBox["7", "4"], "-", FractionBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["3", "2"], "-", "b"]], ",", RowBox[List["2", "-", "b"]]]], "}"]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], "z"]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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 | | HypergeometricPFQ[{},{},z] |  | HypergeometricPFQ[{a},{},z] |  | HypergeometricPFQ[{a},{b},z] |  | HypergeometricPFQ[{a1},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] |  | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] |  |  | 
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