José Antonio Díaz Navas
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 Apr 15 comment Mathematica does not help in this integral I finally got a useful result, see my comment to Dr. Wolfgang Hintze Apr 15 awarded Commentator Apr 15 comment Mathematica does not help in this integral Very nice explanation. It is very interesting that Mathematica finds the correct result with a variable change x=2\[Rho]^2-1. Thus, Integrate[ ((x + 1)/2)^(j/2) x^j/4, {x, -1, 1}, Assumptions -> Element[j, Integers] && j >= 0] gives 2^(-2 - j/2) Gamma[1 + j] (((-1)^j Gamma[1 + j/2])/Gamma[2 + (3 j)/2] + Hypergeometric2F1Regularized[-(j/2), 1 + j, 2 + j, -1]), which solves my problem. Apr 11 accepted Mathematica does not help in this integral Apr 9 comment Mathematica does not help in this integral (3) I have this solution: (2^(-2 - j/2) \[Pi] ((-1)^(1 + j) Csc[(j \[Pi])/2] Gamma[1 + j] + Csc[(3 j \[Pi])/2] (-((Beta[1/2, -1 - (3 j)/2, 1 + j] Gamma[-(j/2)])/Gamma[-1 - (3 j)/2]) + Gamma[1 + j])))/( Gamma[-(j/2)] Gamma[2 + (3 j)/2]) which returns indeterminate for even and odd values for j. However, if you try Table[Integrate[\[Rho]^(j + 1) Sum[Binomial[j, k] (-1)^(j - k) (2 \[Rho]^2)^k, {k, 0, j}, Assumptions -> Element[j, Integers] && j > 0], {\[Rho], 0, 1}, Assumptions -> Element[j, Reals] && j >= 0], {j, 0, 10, 2}], you got useful result. That is why I cannot understand. Apr 9 awarded Curious Apr 8 comment Mathematica does not help in this integral So, zero for even an odd values for 'j'. However, it cannot be as providing values for j from zero to, namely, 10, the integral gives a nonzero value for even 'j'. Apr 8 asked Mathematica does not help in this integral Mar 17 comment mixing color of individual parts of a function in DensityPlot Nice solution. However, why as "raster"? It looses resolution. The alternative as Inset in Graphics seems to be good. Mar 13 accepted mixing color of individual parts of a function in DensityPlot Mar 13 comment mixing color of individual parts of a function in DensityPlot Basically, that is what I did. However, I am also interested in showing the axes for more information about the plot content. Mar 12 asked mixing color of individual parts of a function in DensityPlot Nov 27 awarded Popular Question Nov 14 comment DynamicModule not plotting intersection region? Nice explanation regarding the use of "Dynamic" Nov 14 accepted DynamicModule not plotting intersection region? Nov 13 asked DynamicModule not plotting intersection region? Nov 21 awarded Supporter Oct 6 accepted Am I missing something in this integral? Oct 6 asked Am I missing something in this integral? Jun 28 awarded Scholar