Mathematica Mathematica: Convolution Integral

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The discussion centers around a user's attempt to implement a convolution integral in Mathematica, encountering errors in their code. The user defines functions for a probability density function and a sine function, but receives an error indicating that the integrand is not numerical at certain points. The main issue identified is that the argument of the sine function should be dimensionless; thus, the user needs to multiply k by x instead of dividing k by x. This adjustment is crucial for resolving the error and enabling the plot to display correctly. Suggestions for fixing the code focus on ensuring that all arguments in mathematical functions are appropriately defined to avoid dimensional inconsistencies.
QuantumKnoll
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Hi all! I'm new to Mathematica.
I have written a code for performing a convolution integral (as follows) but it seems to be giving out error messages:

My code is:

a[x_?NumericQ] := PDF[NormalDistribution[40, 2], x]
b[k_?NumericQ, x_?NumericQ] := 0.0026*Sin[1.27*k/x]^2
c[k_?NumericQ, x_?NumericQ] := {a[x]*b[k, x]}
d[k_?NumericQ] := NIntegrate[c[k, x], {x, 0, Infinity}]
Plot [d[k], {k, 0, 350}]

It gives the following error message multiple times:

ntegrand c[0.00715,x] is not numerical at {x} = {124.67}And the plot dosen't show up..!
Does anyone have any suggestions on how to fix it ?
 
Last edited:
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The argument of the sin function is wrong. It must be dimensionless, i.e. k multiplied by x not divided by x.
 

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