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Lapsed engineer/scientist (now a patent practitioner) seeking to expand his math skills. Most of those skills lay in areas useful in optics such as sums & integrals (like the one below), complex analysis, differential equations, transforms, and data analysis.

My greatest hits page. (a work in progress)

"Wir müssen wissen, wir werden wissen." - David Hilbert

The picture on the left represents the integration region for the following integral of functions of finite support:

$$T(\mathbf{u}',\mathbf{u}'') = \int_{\mathbb{R}^2} d^2 \mathbf{\sigma} \; S(\mathbf{\sigma}) P(\mathbf{u}'+\mathbf{\sigma}) P^*(\mathbf{u}''+\mathbf{\sigma})$$


Sep
12
revised How do I evaluate this integral $\int_0^\pi{\frac{{{x^2}}}{{\sqrt 5-2\cos x}}}\operatorname d\!x$?
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Sep
12
awarded  Nice Answer
Sep
9
awarded  Nice Answer
Sep
8
awarded  Enlightened
Sep
8
awarded  Nice Answer
Sep
5
awarded  Enlightened
Sep
3
comment Complex Integrals using a contour
math.stackexchange.com/questions/392580/…
Aug
27
answered Understanding APR - can it be calculated as a dollar amount
Aug
27
revised Using Fourier Transform to solve heat equation
added 1 character in body
Aug
26
comment Using Fourier Transform to solve heat equation
@leave2014: in any book on FT's.
Aug
26
comment Using Fourier Transform to solve heat equation
@leave2014: it should work out all the same, but you restricted yourself to positive $x$. Thus, when you integrated by parts, you ended up with this unknowable boundary value at $x=0$.
Aug
26
revised Using Fourier Transform to solve heat equation
added 162 characters in body
Aug
26
revised Using Fourier Transform to solve heat equation
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Aug
26
answered Using Fourier Transform to solve heat equation
Aug
24
awarded  Enlightened
Aug
23
awarded  Nice Answer
Aug
18
comment Need help with $\int_0^\infty\frac{\log(1+x)}{\left(1+x^2\right)\,\left(1+x^3\right)}dx$
@Superabound: it's due to the form of the summand. In other words, write out the terms of the sum and see how you can make the replacement.
Aug
14
awarded  Guru
Aug
11
comment Interesting log sine integrals $\int_0^{\pi/3} \log^2 \left(2\sin \frac{x}{2} \right)dx= \frac{7\pi^3}{108}$
@ChantryCargill: much appreciated! The identity comes from the Taylor series for $(1-x)^{-1/2}$ about $x=0$.
Aug
3
comment The limit of the product $\prod_{i=1}^n\frac{1 - (2i + 1)a/(2n)}{1 - ia/n}$ as $n\to\infty$
@did: thanks for pushing me to improve the post.