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variants of this functions
BetaRegularized






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > BetaRegularized[z,a,b] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/06.21.13.0005.01









  


  










Input Form





Derivative[2][w][z] - h[z] ((2 Derivative[1][h][z])/h[z]^2 + ((1 - a + (-2 + a + b) g[z]) Derivative[1][g][z])/ ((-1 + g[z]) g[z] h[z]) + Derivative[2][g][z]/ (h[z] Derivative[1][g][z])) Derivative[1][w][z] + ((2 Derivative[1][h][z]^2)/h[z]^2 + ((1 - a + (-2 + a + b) g[z]) Derivative[1][g][z] Derivative[1][h][z])/((-1 + g[z]) g[z] h[z]) + (Derivative[2][g][z] Derivative[1][h][z])/(h[z] Derivative[1][g][z]) - Derivative[2][h][z]/h[z]) w[z] == 0 /; w[z] == Subscript[c, 1] h[z] + Subscript[c, 2] h[z] BetaRegularized[g[z], a, b]










Standard Form





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MathML Form







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</mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </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> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <msub> <mi> c </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> h </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <mrow> <mi> g </mi> <mo> &#8289; 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Rule Form





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





2007-05-02