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Mar
17
comment Any way to simplify integral of Confluent Hypergeometric Function of the First Kind?
@NathanMcKenzie out of interest, from what problem does this integral arise?
Mar
17
comment Any way to simplify integral of Confluent Hypergeometric Function of the First Kind?
You may have better luck using the change of variable $y=\frac{\log n}{t}+1$. This gives $dt=\frac{\log(n)dy}{y^2}$ and $t=-\log n\implies y=0$, $t=0\implies y=\infty$. Then the integral becomes: $$-z\log(n)\int_0^\infty \frac{e^{\frac{\log (n)(1-s)}{y-1}}}{(y-1)^2} {}_1F_1\left(1-z,2,\frac{\log n}{y-1}\right)dy.$$ There are plenty of tables of integrals with limits over $\mathbb{R}^+$. See e.g. Gradshteyn and Ryzhik, p.814.
Mar
11
revised Is there a name for an object with both position and velocity?
edited tags
Mar
11
comment Is there a name for an object with both position and velocity?
@Sebastian, so for example a point in phase space might be $p=(x,y,u,v)$, where $(x,y)$ is position and $(u,v)$ is velocity. Thank you.
Mar
11
asked Is there a name for an object with both position and velocity?
Feb
26
comment Does the integral $\int_{1}^{\infty} \sin(x\log x) \,\mathrm{d}x$ converge?
I understand you're using the Lambert W function which enables you to obtain $x=g(y)$, but could you please explain in a little more detail how you got the substituted integral?
Feb
23
revised Riemann Zeta Function and Including Complex Numbers
added 9 characters in body
Feb
23
answered Riemann Zeta Function and Including Complex Numbers
Feb
21
accepted Examples of orthogonal/orthonormal functions which are not finite degree polynomials?
Feb
19
comment What is known about the complex solutions to $\zeta(s)=-1$?
I suppose this is related to "level curves" of a function...
Feb
19
revised What is known about the complex solutions to $\zeta(s)=-1$?
added 171 characters in body
Feb
19
accepted What is known about the complex solutions to $\zeta(s)=-1$?
Feb
19
revised What is known about the complex solutions to $\zeta(s)=-1$?
edited title
Feb
19
comment What is known about the complex solutions to $\zeta(s)=-1$?
My thoughts too. I was just wondering if there was anything in the literature on this "other case". Are there multiple solutions or just one solution, etc. For example, in the case $\zeta(s)=0$ it is known that there are an infinite number of such $s$ on the critical line. NB I've changed the title to reflect what I'm trying to get at.
Feb
19
asked What is known about the complex solutions to $\zeta(s)=-1$?
Feb
16
revised Can a substitution cause a convergent definite integral to diverge?
added 364 characters in body
Feb
11
comment How do you define the derivative of a function without an argument?
Maybe Differential Fields, with the operator $D$ is what you're looking for.
Feb
4
comment Proof of the limit using only elementary techniques
@TonyK ok yes not a limit ("tends to") - my mistake. But maybe it is approximately $e^n$.
Feb
4
comment Proof of the limit using only elementary techniques
Does this imply $\text{lcm}(1,2,\ldots,n)\to e^n$ as $n\to\infty$ ?
Feb
4
revised Complex integration identity
added 1 character in body