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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 $?
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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?
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?
Dec
20
revised Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers?
edited title
Dec
20
revised Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers?
deleted 38 characters in body
Dec
20
asked Could “$\infty$” be understood by taking the reciprocals of the Hyperreal numbers?
Dec
19
awarded  Constituent
Dec
16
comment Is the derivative of $\{x\}$ on $(0,1)$ always equal to $1$?
Yes, sorry - question updated. Thanks for spotting this.
Dec
8
awarded  Caucus
Dec
7
awarded  Nice Answer
Nov
26
awarded  Notable Question