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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,lambda,z] > Specific values > Specialized values > For fixed lambda, z





http://functions.wolfram.com/07.03.03.0016.01









  


  










Input Form





LaguerreL[7, \[Lambda], z] == (1/5040) (-z^7 + 7 z^6 (7 + \[Lambda]) - 21 z^5 (42 + 13 \[Lambda] + \[Lambda]^2) + 35 z^4 (210 + 107 \[Lambda] + 18 \[Lambda]^2 + \[Lambda]^3) - 35 z^3 (840 + 638 \[Lambda] + 179 \[Lambda]^2 + 22 \[Lambda]^3 + \[Lambda]^4) + 21 z^2 (2520 + 2754 \[Lambda] + 1175 \[Lambda]^2 + 245 \[Lambda]^3 + 25 \[Lambda]^4 + \[Lambda]^5) - 7 z (5040 + 8028 \[Lambda] + 5104 \[Lambda]^2 + 1665 \[Lambda]^3 + 295 \[Lambda]^4 + 27 \[Lambda]^5 + \[Lambda]^6) + 5040 + 13068 \[Lambda] + 13132 \[Lambda]^2 + 6769 \[Lambda]^3 + 1960 \[Lambda]^4 + 322 \[Lambda]^5 + 28 \[Lambda]^6 + \[Lambda]^7)










Standard Form





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MathML Form







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</ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 107 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 210 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 22 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 179 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 638 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 840 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> <apply> <times /> <cn type='integer'> 25 </cn> <apply> <power /> <ci> &#955; 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</ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5104 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8028 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 5040 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 7 </cn> </apply> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 322 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1960 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6769 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13132 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13068 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 5040 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LaguerreL", "[", RowBox[List["7", ",", "\[Lambda]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", SuperscriptBox["z", "7"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "6"], " ", RowBox[List["(", RowBox[List["7", "+", "\[Lambda]"]], ")"]]]], "-", RowBox[List["21", " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["42", "+", RowBox[List["13", " ", "\[Lambda]"]], "+", SuperscriptBox["\[Lambda]", "2"]]], ")"]]]], "+", RowBox[List["35", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["210", "+", RowBox[List["107", " ", "\[Lambda]"]], "+", RowBox[List["18", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", SuperscriptBox["\[Lambda]", "3"]]], ")"]]]], "-", RowBox[List["35", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["840", "+", RowBox[List["638", " ", "\[Lambda]"]], "+", RowBox[List["179", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["22", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", SuperscriptBox["\[Lambda]", "4"]]], ")"]]]], "+", RowBox[List["21", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["2520", "+", RowBox[List["2754", " ", "\[Lambda]"]], "+", RowBox[List["1175", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["245", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["25", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", SuperscriptBox["\[Lambda]", "5"]]], ")"]]]], "-", RowBox[List["7", " ", "z", " ", RowBox[List["(", RowBox[List["5040", "+", RowBox[List["8028", " ", "\[Lambda]"]], "+", RowBox[List["5104", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["1665", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["295", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["27", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", SuperscriptBox["\[Lambda]", "6"]]], ")"]]]], "+", "5040", "+", RowBox[List["13068", " ", "\[Lambda]"]], "+", RowBox[List["13132", " ", SuperscriptBox["\[Lambda]", "2"]]], "+", RowBox[List["6769", " ", SuperscriptBox["\[Lambda]", "3"]]], "+", RowBox[List["1960", " ", SuperscriptBox["\[Lambda]", "4"]]], "+", RowBox[List["322", " ", SuperscriptBox["\[Lambda]", "5"]]], "+", RowBox[List["28", " ", SuperscriptBox["\[Lambda]", "6"]]], "+", SuperscriptBox["\[Lambda]", "7"]]], "5040"]]]]]










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





2001-10-29





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