![](/common/images/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
http://functions.wolfram.com/07.17.26.0066.01
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
Sin[z] Hypergeometric0F1[b, -(z^2/4)] == 2^(-(3/2) + b) Gamma[b]
MeijerG[{{(1/4) (3 - 2 b), (1/4) (5 - 2 b)}, {}},
{{1/2}, {0, 1 - b, 3/2 - b}}, z, 1/2]
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
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[SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", "b"]]], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "b"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", "b"]], ",", RowBox[List[FractionBox["3", "2"], "-", "b"]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]]]]]]
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
<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> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </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]", FormBox["0", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[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> <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> <mrow> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <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> <mrow> <mi> z </mi> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn> 3 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mn> 4 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mn> 5 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mn> 4 </mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> </mrow> <mo> , </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <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[RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox[RowBox[List["3", "-", RowBox[List["2", "b"]]]], "4"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["5", "-", RowBox[List["2", "b"]]]], "4"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "b"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", "b"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <times /> <ci> sin </ci> <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> <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> <times /> <ci> Γ </ci> <ci> b </ci> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list /> </list> <list> <list> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list> <cn type='integer'> 0 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <plus /> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </list> </list> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/clear.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| | ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| 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]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "+", "b"]]], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "b"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", RowBox[List["1", "-", "b"]], ",", RowBox[List[FractionBox["3", "2"], "-", "b"]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]]]]]] |
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
| ![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
Date Added to functions.wolfram.com (modification date)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
![](/images/home/spacer.gif)
|
|
![](/common/images/spacer.gif) |
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] | |
|
|
|