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  • 0 posts edited
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  • 11 votes cast
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