- #1
beautiful1
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I am looking for help with the following integral
[tex] A = \int dx \int dy \exp(-a (x+y)^2 +ib(x-y)) sinc(cx+dy) sinc(dx+cy) [/tex]
where [tex] sinc(x) =\sin(x) / x [/tex] for [tex] x \neq 0 [/tex] and [tex] sinc(0) = 1 [/tex]
(pls forgive my poor latex)
Either in the indefinite form or with the upper/lower limits at [tex]+/-\infty [/tex]
The real-valued constants [tex] a, b, c, [/tex] and [tex] d [/tex] are positive.
My original idea was to switch to coordinates [tex] w = x+y [/tex] and [tex] u=x-y [/tex] but I can not get pass the sinc functions...any help would be appreciated.
[tex] A = \int dx \int dy \exp(-a (x+y)^2 +ib(x-y)) sinc(cx+dy) sinc(dx+cy) [/tex]
where [tex] sinc(x) =\sin(x) / x [/tex] for [tex] x \neq 0 [/tex] and [tex] sinc(0) = 1 [/tex]
(pls forgive my poor latex)
Either in the indefinite form or with the upper/lower limits at [tex]+/-\infty [/tex]
The real-valued constants [tex] a, b, c, [/tex] and [tex] d [/tex] are positive.
My original idea was to switch to coordinates [tex] w = x+y [/tex] and [tex] u=x-y [/tex] but I can not get pass the sinc functions...any help would be appreciated.
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