I have a convex optimization problem of finding a function Q(x,y) as below: Minimize $\int{k(x,y)Q(x,y)dxdy}$ subject to a list of constraints which are not relevant to the questi …

Mamikon's visual calculus (see Mamikon, Tom Apostol, Wikipedia) is a very beautiful and surprisingly efficient tool. The basis is Mamikon's theorem. The area of a tangent swee …

recently, i need to compute this kind of integral: $$ \int ^\infty _c \Phi(ax+b) \phi(x) dx$$ where a, b and c are all constants and $\Phi(x)$ denotes the CDF of standard normal di …

By using the Iwasawa decomposition, one obtains a (bi-invariant) Haar measure on $G:=\mathrm{SL}(2,\mathbb{R})$ which can be symbolically written as $\mathrm{d}x=\mathrm{d}a\,\math …

I asked the same question on math.se but got no answer there. Since it pertains to my current research, I decided to ask here: Let $n\in 2\mathbb{N}$ be an even number. I want to …

Let $f$ be a bounded function on a close interval, $[0,1]$ e.g.. Can it be everywhere discontinuous and integrable? Thanks! P.S. It isn't a homework for me and I asked this quest …

In the paper E. Mehlum, Appell and the apple (nonlinear splines in space), Technical Report No. 1676 (1981), Central institute for industrial research, Oslo (reproduced in the book …

Hello! In textbooks Stokes theorem is usually formulated for orientable manifolds (At least I couldn't find any version not using orientability). Is Stokes theorem: $\int\limits_{ …

let be the integral $$ \int_{0}^{\infty}dx\int_{0}^{\infty}dy\int_{0}^{\infty}dz \frac{f(x,y,z)}{(1+x^{2}+y^{2}+z^{2})^{s}} $$ here $ s $ is a parameter so the integral converges …

How do I solve the Integral $$ \frac{1}{2\pi j} \oint \frac{b^{ - s} \Gamma[2 + i - s] \Gamma[s] \Gamma[-1 - i + s]}{ (2 + i - s) \Gamma[3 + i - s]} \:\mathrm{d}s$$ This integral …

Sometimes definite integral is defined using antiderivatives: $$\int_{a}^b{f(t)dt}=F(b)-F(a)$$ where $F$ is any continuous function such that: $$(\forall t\in[a,b]\setminus C)(F'( …

I've been trying to find a closed form expression/series expansion for the following integral without success: $$F(a,b)=\int_{\epsilon-i\infty}^{\epsilon+i\infty} e^{az+b^2z^2}\Ga …

I posted this question to stackexchange and after 24 hours it's got five votes and no answers, so let's see if mathoverflow can say more than that. Consider two propositions in ge …

Possible Duplicate: Why is differentiating mechanics and integration art? There is a formula for the derivative of any product, composite or sum of functions, in terms of …

I have the following sum $\sum_{j=1}^K {K \choose j} (-1)^{j+1}/j$. Now I can write this as the integral $\int_{-1}^0 \frac{(1+x)^K - 1}{x} dx$. However, I wonder whether there is …