I have a integral after convolution where there is a term of Sin[\pi x]/x . I want the final integral in terms of Sinc[x] function. Is there a way to manipulate the expression so that possible Sin[pi x]/x gets replaced by Sinc.
Edit1- Suppose like I get the answer of the integral
\exp(i2\pi ft)\frac{\sin(\pi k x)}{x} \;
I just want to convert to get the final answer in Sinc[x]. So the final answer that should come is k\pi\exp(i2\pi ft) \text{Sinc}(\pi k x) \;.
Also, apart from above is there something in Mathematica like rewrite (https://in.mathworks.com/help/symbolic/rewrite.html) command in Matlab.
Both like the examples are different. I was just trying to give examples of what I need. I just need whenever there is something like \sin(k\; x)/x where k is a constant then it should get replaced by k*Sinc[x].
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Maybe like so:
expr[Sin[Pi x]/x] /. Sin[a_] :> a Sinc[a]
I have edited the question. Can you please take a look?
I have edited the question. Can you take a look now if you know the answer.
It would really help people that are trying to help you if you post the WL code you have tried, not LaTeX.
ClearAll[f, t, k, x]
exp = Exp[2 Pi I f t] Sin[Pi k x]/x;
exp /. Sin[e_]/x -> Sinc[e]
(* E^(2 I f π t) Sinc[k π x] *)
Why does your desired output in LaTeX have a k π factor? That does not match the description of the desired output.
@Rohit Namjoshi I was just trying to give example. I was trying to say if I have anything like sin(k x)/x where k is a constant it should get replaced by a k Sinc[x].
exp /. Sin[k_ x]/x → k Sinc
Thanks. I didn’t know that you can do something like Sin[k_ x]. I always used to think like thisSin[k_].