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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case 1F~2





http://functions.wolfram.com/07.32.03.0095.01









  


  








Input Form





HypergeometricPFQRegularized[{3/4}, {3/2, 7/4}, z] == (1/(Sqrt[2] z^(3/4) Gamma[3/4])) (Erfi[Sqrt[2] z^(1/4)] - Erf[Sqrt[2] z^(1/4)])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", FractionBox["3", "4"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]]]]], RowBox[List["(", RowBox[List[RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]], "-", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 1 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> ; </mo> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 7 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;1&quot;, TraditionalForm]], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], FormBox[&quot;2&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[TagBox[FractionBox[&quot;3&quot;, &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;7&quot;, &quot;4&quot;], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, HypergeometricPFQRegularized, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <cn type='rational'> 3 <sep /> 4 </cn> </list> <list> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 4 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Erf </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", FractionBox["3", "4"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Erfi", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]], "-", RowBox[List["Erf", "[", RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], "]"]]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]]]]]]]]]


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





2001-10-29