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 Jan17 comment Examples of orthogonal/orthonormal functions which are not finite degree polynomials? Ah I see. Is this related to the so-called Schmidt process? (related to Gram-Schmidt by any chance...) Jan17 revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials? added 1 character in body Jan17 revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials? added 64 characters in body Jan17 revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials? added 57 characters in body Jan17 revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials? edited title Jan17 asked Examples of orthogonal/orthonormal functions which are not finite degree polynomials? Jan15 comment How to prove that $\left(\sqrt{3}\sec{\frac{\pi}{5}}+\tan{\frac{\pi}{30}}\right)\tan{\frac{2\pi}{15}}=1$ In general, squaring and applying known trigonometric identities can sometimes be of help. Might not be of help here though. Jan13 comment How do I find the equivalence of the expression $e^{n\log(n)-(n+e)\log(n + e)}$? Do you mean you want to find an asymptotic formula for the expression? Jan13 comment Unusual mathematical terms The `Golden ratio' $\phi$. Jan13 revised The gradient of a distance function. added 22 characters in body Jan13 comment Integer root of a quadratic Do you mean over all $a\in\mathbb{Z}$ or just some specific $a\in\mathbb{Z}$ for which $n^2-an+6a=0$ has integer solution(s) $n$ ? If it's a specific $a$ then don't you just need to use the quadratic formula, assuming your integer $a$ gives integer solutions for $n$? Jan12 comment Gradient of product of sums Maybe the product rule? $(u\cdot v)'=u\cdot v'+v\cdot u'$ ? Jan11 revised Find appropriate substitution for indefinite integral. edited body Jan8 revised How to calculate $\int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx$? added 71 characters in body Jan8 revised How to calculate $\int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx$? added 5 characters in body Jan7 answered How to calculate $\int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx$? Jan7 comment Is there a domain “larger” than (i.e., a supserset of) the complex number domain? There are also the Quarternions ($z=a+ib+jc+kd\equiv(a,b,c,d)$), Octonions, and so on, each of which is a generalisation of the complex numbers. Each generalisation, however, loses some nice property of the "previous" set of numbers, e.g. commutatvity, and so on. I don't recall the exact details. Jan6 comment How to calculate $\int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx$? Using the binomial theorem $$I=\sum_{k=0}^{2r-1}{2r-1\choose k}\int_0^1 \frac{x^k}{1+x^2}dx.$$ Taking $k$ even and odd separately gives "nice" values, although I don't have time to work out their closed forms right now. What have you tried so far? Dec22 comment Nice approximations of sums by integrals. Have you tried using the Euler-Maclaurin summation formula? A Google search will give further details (en.m.wikipedia.org/wiki/Euler–Maclaurin_formula) Dec20 accepted Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers?