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Jan
17
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...)
Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
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Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
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Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
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Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
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Jan
17
asked Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
Jan
15
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.
Jan
13
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?
Jan
13
comment Unusual mathematical terms
The `Golden ratio' $\phi$.
Jan
13
revised The gradient of a distance function.
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Jan
13
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 $n$?
Jan
12
comment Gradient of product of sums
Maybe the product rule? $(u\cdot v)'=u\cdot v'+v\cdot u'$ ?
Jan
11
revised Find appropriate substitution for indefinite integral.
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Jan
8
revised How to calculate $ \int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx $?
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Jan
8
revised How to calculate $ \int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx $?
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Jan
7
answered How to calculate $ \int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx $?
Jan
7
comment Is there a domain “larger” than (i.e., a supserset of) the complex number domain?
There are also the Quarternions ($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.
Jan
6
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?
Dec
22
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)
Dec
20
accepted Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers?