Reputation
3,020
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
9 28
Newest
 Nice Answer
Impact
~102k people reached

Jan
18
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
edited tags
Jan
18
asked Is there a name for functions “opposite in nature” to orthogonal functions?
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?
added 1 character in body
Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
added 64 characters in body
Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
added 57 characters in body
Jan
17
revised Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
edited title
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.
added 22 characters in body
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.
edited body
Jan
8
revised How to calculate $ \int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx $?
added 71 characters in body
Jan
8
revised How to calculate $ \int_0^1 \frac{(1+x)^{2r-1}}{1+x^2}dx $?
added 5 characters in body
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?