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 | | http://functions.wolfram.com/05.02.21.0007.01 | 
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 | | Integrate[(z^(\[Alpha] - 1) LaguerreL[n, c z])/E^(c z), z] == 
 z^\[Alpha] Gamma[\[Alpha]] HypergeometricPFQRegularized[{1 + n, \[Alpha]}, 
   {1, 1 + \[Alpha]}, (-c) z] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", "z"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n", ",", RowBox[List["c", " ", "z"]]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["Gamma", "[", "\[Alpha]", "]"]], "  ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", "n"]], ",", "\[Alpha]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "+", "\[Alpha]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "c"]], " ", "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>  <mrow>  <mo> ∫ </mo>  <mrow>  <msup>  <mi> z </mi>  <mrow>  <mi> α </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> L </mi>  <mi> n </mi>  </msub>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ⅆ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <msup>  <mi> z </mi>  <mi> α </mi>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> α </mi>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mi> n </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mi> α </mi>  </mrow>  <mo> ; </mo>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mrow>  <mi> α </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["n", "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["\[Alpha]", HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["\[Alpha]", "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[RowBox[List[RowBox[List["-", "c"]], " ", "z"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation>  </semantics>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <int />  <bvar>  <ci> z </ci>  </bvar>  <apply>  <times />  <apply>  <power />  <ci> z </ci>  <apply>  <plus />  <ci> α </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <power />  <exponentiale />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <ci> LaguerreL </ci>  <ci> n </ci>  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <ci> z </ci>  <ci> α </ci>  </apply>  <apply>  <ci> Gamma </ci>  <ci> α </ci>  </apply>  <apply>  <ci> HypergeometricPFQRegularized </ci>  <list>  <apply>  <plus />  <ci> n </ci>  <cn type='integer'> 1 </cn>  </apply>  <ci> α </ci>  </list>  <list>  <cn type='integer'> 1 </cn>  <apply>  <plus />  <ci> α </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c_"]], " ", "z_"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", RowBox[List["c_", " ", "z_"]]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", "\[Alpha]"], " ", RowBox[List["Gamma", "[", "\[Alpha]", "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", "n"]], ",", "\[Alpha]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["1", "+", "\[Alpha]"]]]], "}"]], ",", RowBox[List[RowBox[List["-", "c"]], " ", "z"]]]], "]"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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