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 Apr 27 revised On the solution of Volterra integral equation added 181 characters in body Apr 27 answered On the solution of Volterra integral equation Apr 27 comment On the solution of Volterra integral equation Where is your Volterra operator defined? On which algebra of functions are you seeking a solution to this integral equation? Apr 19 comment criteria of convergence of a series Use the integral test followed by the change of variable $x = \ln(t)$ Apr 17 answered Does $\int _1 ^\infty\frac {f(x)} x\,dx$ converge or diverge? Apr 17 comment If $f$ is entire and $\lim_{z\to\infty} \frac{f(z)}{z} = 0$ show that $f$ is constant Yet another method might be to consider the function $g(z) := f(\frac{1}{z})$ and prove that g is entire (only have to check that g has a removable singularity at 0). Now go back to the Taylor expansion of f at $\infty$ and conclude Apr 9 comment What does it mean “a Lebesgue point of $f$”? It is the same thing, we just expressed it in terms of the definition of a limit. Notice that $L^{p}_{loc} \subset L^{1}_{loc}$ for $p\geq 1$ Apr 6 comment Prove $\sum_{k=0}^{n}{n \choose k}(-1)^k \frac{1}{k+1} = \frac{1}{n+1}$ Interchange the integral with the sum and use the binomial theorem Mar 26 comment Old & cool integral $\int_0^{\pi} \sin^{b-1}(x) \sin(a x) \ dx=\frac{\pi \sin(a \pi/2)}{2^{b-1}b B\left(\frac{b+a+1}{2},\frac{b-a+1}{2}\right)}$ Have you tried using the Fourier series expansion of $\sin(ax)$ ? Feb 4 comment Computation of an iterated integral Very good Answer! (+1) Feb 2 comment If $f(x)$ is continuous at $x=0$ Your assumtion is that $f = O(x^{2})$ near $x=0$ Jan 30 answered Reflexive Banach spaces, compactness Jan 30 answered Problem calcualting Fourier coeff. of tent function. Jan 22 comment Do these series converge uniformly? Hints: For the first one, what can be said about the series for $x\leq 0$? For the second one, try splitting the sum Jan 11 revised Integration of $\int_0^{+\infty} \frac{\ln(1/x)}{1-x^2}\,dx$ added 2 characters in body; added 88 characters in body Jan 11 answered Integration of $\int_0^{+\infty} \frac{\ln(1/x)}{1-x^2}\,dx$ Jan 10 comment Deciding whether a function $f$, defined on $\mathbb{R}^2$, is Lebesgue-integrable over two sets For (ii): If $f(x,y)$ where integrable, then the integral of $|f(x,y)|$ over $A$ should be finite, independent of the order of integration. But.. Jan 10 comment Prove that $τ(m^n)$ and $n$ are coprime $(m,n ∈ N^+)$ $m^{n}$ might have more distinct divisors, if say $m$ is not a prime. But there is a way to work around it, by utilizing the multiplicativity of $\tau$ Jan 7 revised On uniqueness of extension of linear functional on $\ell^{1}$ added 29 characters in body Jan 5 comment Show that $\int_0^1 f(x)g(x)\,dx=0$ for all $g\in C([0,1])$ implies $f=0$ almost everywhere Well, that works as long as we remain continuous.