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Apr
3
answered Relationship between ord($a$) and ord($a^k$)
Apr
3
awarded  Nice Question
Apr
3
comment Is there a slowest rate of divergence of a series?
@user139964 This is interesting. Can one construct an infinite sequence of series, each term diverging slower than the last, using the Ackermann function?
Apr
2
asked This $\int_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \frac{e^{in x}dx}{1+\tan^m(x)}$ integral: does a closed form exist?
Apr
2
comment What is $\sum_{n=0}^{\infty}|a_nz^n|^2=\frac{1}{2 \pi}\int_{-\pi}^{\pi}|f(ze^{it})|^2dt$ for?
This is related, in case you didn't already know.
Apr
2
answered What is $\sum_{n=0}^{\infty}|a_nz^n|^2=\frac{1}{2 \pi}\int_{-\pi}^{\pi}|f(ze^{it})|^2dt$ for?
Apr
2
comment Closed form or asymptotic expansion for $\int_0^m \frac{n^x}{\Gamma(x+1)}dx$?
Yes, I thought of it after making my request more precise to Antonio.
Apr
2
comment Closed form or asymptotic expansion for $\int_0^m \frac{n^x}{\Gamma(x+1)}dx$?
@AntonioVargas Sorry, I meant $n \to \infty$ with constant $m$.
Apr
2
revised Closed form or asymptotic expansion for $\int_0^m \frac{n^x}{\Gamma(x+1)}dx$?
added 5 characters in body; edited title
Apr
2
comment Closed form or asymptotic expansion for $\int_0^m \frac{n^x}{\Gamma(x+1)}dx$?
@AntonioVargas I was referring to asymptotic expansions (as described here), I'll edit the question accordingly. I grant that $\sum_{i=0}^{m-1}\frac{n^i}{i!}$ may not be the first term of an asymptotic expansion for the integral, it was just an idea.
Apr
2
comment Closed form or asymptotic expansion for $\int_0^m \frac{n^x}{\Gamma(x+1)}dx$?
@AntonioVargas Ideally for all $m$.
Apr
2
asked Closed form or asymptotic expansion for $\int_0^m \frac{n^x}{\Gamma(x+1)}dx$?
Apr
1
awarded  Great Answer
Mar
31
comment Prove that $\int_0^{\pi/2} \cos^{p+q-2}(\theta) \cos((p-q)\theta)d\theta = \frac{\pi}{(p+q-1)2^{p+q-1}B(p,q)}$
Related: math.stackexchange.com/questions/718610/….
Mar
31
comment A nice form for this Beta-like integral $\int_0^\frac{\pi}{2} \sin^\alpha(n t) \cos^\beta(t)dt$?
@HarryPeter Indeed that comment seems silly now, my doubts were certainly correct then.
Mar
29
comment Prove that $\Gamma(p)\times \Gamma(1-p)=\frac{\pi}{\sin (p\pi)},\: \forall p \in (0,\: 1)$
How does one prove that it's bounded?
Mar
28
comment Intuitive basis of Mobius inversion?
@SpamIAm Do you mean p. 66? I've not, but looking through it, it doesn't seem a massive improvement on the standard convolution method.
Mar
27
accepted Proving $\frac{\cos(t \arctan(\sqrt{x}))}{(1+x)^{t/2}}= \sum_{k \ge 0}\frac{\Gamma(t+2k)\Gamma(k+1)}{\Gamma(t)\Gamma(2k+1)}\frac{(-x)^k}{k!}$
Mar
25
comment infinite sum and integral representation
Are you using $x_n$ as the $n$th falling factorial of $x$?
Mar
24
accepted Isomorphism between this subgroup of complex numbers and all finitely generated abelian groups ?