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Hypergeometric Functions
 
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r]
 
Specific values
 
Specialized values
 
Case {m,n,p,q}={1,0,1,3}
 
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   http://functions.wolfram.com/07.35.03.0049.01
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    MeijerG[{{}, {a}}, {{a - 1/4}, {a - 1, a - 3/4}}, z, 1/4] == 
 (-((1 + I)/Pi)) z^(4 (-1 + a)) FresnelS[(1 + I) Sqrt[2/Pi] z] 
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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>  <semantics>  <mrow>  <msubsup>  <mi> G </mi>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mn> 3 </mn>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mn> 0 </mn>  </mrow>  </msubsup>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> ❘ </mo>  <mtable>  <mtr>  <mtd>  <mi> a </mi>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mfrac>  <mn> 3 </mn>  <mn> 4 </mn>  </mfrac>  </mrow>  </mrow>  </mtd>  </mtr>  </mtable>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "3"]], RowBox[List["1", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[TagBox["a", MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox[RowBox[List["a", "-", FractionBox["1", "4"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "-", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "-", FractionBox["3", "4"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 1 </mn>  <mo> + </mo>  <mi> ⅈ </mi>  </mrow>  <mi> π </mi>  </mfrac>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <semantics>  <mi> S </mi>  <annotation encoding='Mathematica'> TagBox["S", FresnelS] </annotation>  </semantics>  <mo> ( </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> + </mo>  <mi> ⅈ </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msqrt>  <mfrac>  <mn> 2 </mn>  <mi> π </mi>  </mfrac>  </msqrt>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> MeijerG </ci>  <list>  <list />  <list>  <ci> a </ci>  </list>  </list>  <list>  <list>  <apply>  <plus />  <ci> a </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  </apply>  </list>  <list>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <plus />  <ci> a </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 3 <sep /> 4 </cn>  </apply>  </apply>  </list>  </list>  <ci> z </ci>  <cn type='rational'> 1 <sep /> 4 </cn>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <imaginaryi />  </apply>  <apply>  <power />  <pi />  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> FresnelS </ci>  <apply>  <times />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <imaginaryi />  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <pi />  <cn type='integer'> -1 </cn>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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   Date Added to functions.wolfram.com (modification date)
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| MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] |  |   |  
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