pbs
Reputation
2,592
Top tag
Next privilege 3,000 Rep.
 Mar17 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? Mar17 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. Mar11 revised Is there a name for an object with both position and velocity? edited tags Mar11 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. Mar11 asked Is there a name for an object with both position and velocity? Feb26 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? Feb23 revised Riemann Zeta Function and Including Complex Numbers added 9 characters in body Feb23 answered Riemann Zeta Function and Including Complex Numbers Feb21 accepted Examples of orthogonal/orthonormal functions which are not finite degree polynomials? Feb19 comment What is known about the complex solutions to $\zeta(s)=-1$? I suppose this is related to "level curves" of a function... Feb19 revised What is known about the complex solutions to $\zeta(s)=-1$? added 171 characters in body Feb19 accepted What is known about the complex solutions to $\zeta(s)=-1$? Feb19 revised What is known about the complex solutions to $\zeta(s)=-1$? edited title Feb19 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. Feb19 asked What is known about the complex solutions to $\zeta(s)=-1$? Feb16 revised Can a substitution cause a convergent definite integral to diverge? added 364 characters in body Feb11 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. Feb4 comment Proof of the limit using only elementary techniques @TonyK ok yes not a limit ("tends to") - my mistake. But maybe it is approximately $e^n$. Feb4 comment Proof of the limit using only elementary techniques Does this imply $\text{lcm}(1,2,\ldots,n)\to e^n$ as $n\to\infty$ ? Feb4 revised Complex integration identity added 1 character in body