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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/07.09.13.0005.01









  


  








Input Form





h[z]^2 Derivative[1][g][z] Derivative[2][w][z] - (2 h[z] Derivative[1][g][z] Derivative[1][h][z] + h[z]^2 ((2 g[z] Derivative[1][g][z]^2)/(1 - g[z]^2) + Derivative[2][g][z])) Derivative[1][w][z] + (-(((\[Mu]^2 - \[Nu] (1 + \[Nu]) (1 - g[z]^2)) h[z]^2 Derivative[1][g][z]^3)/(1 - g[z]^2)^2) + 2 Derivative[1][g][z] Derivative[1][h][z]^2 + h[z] (Derivative[1][h][z] ((2 g[z] Derivative[1][g][z]^2)/(1 - g[z]^2) + Derivative[2][g][z]) - Derivative[1][g][z] Derivative[2][h][z])) w[z] == 0 /; w[z] == Subscript[c, 1] h[z] LegendreP[\[Nu], \[Mu], 3, g[z]] + Subscript[c, 2] h[z] LegendreQ[\[Nu], \[Mu], 3, g[z]]








Standard Form





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MathML Form







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</mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <msup> <mi> g </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> h </mi> <mi> &#8242;&#8242; </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#63449; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#63449; </mo> <mrow> <mrow> <msub> <mi> c </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox[&quot;P&quot;, LegendreP] </annotation> </semantics> <mi> &#957; 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</ci> <ci> &#956; </ci> <cn type='integer'> 3 </cn> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> h </ci> <ci> z </ci> </apply> <apply> <ci> LegendreQ </ci> <ci> &#957; </ci> <ci> &#956; </ci> <cn type='integer'> 3 </cn> <apply> <ci> g </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02