# Tagged Questions

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### A functional inequality

$g:[0,1]\to[0,1]$ continuously differentiable and increasing such that for all integers $t>0$ and for all $r\in(0,1)$, $g(r^{t+1})>g(r)\cdot g(r^t)$. Does this imply that for all ...
Good day to everyone. In my scientific research I've got stuck with a contour integration problem. I would like to evaluate the following integral: $$I=\int_0^{\infty } \frac{e^{\frac{\alpha -\mathrm ... 1answer 162 views ### Limit involving regularlized gamma function and its inverse Let$$L(x)=Q\left(\frac{x}{2},\frac{a}{a+f(x)/\sqrt{x}}Q^{-1}\left(\frac{x}{2},1-b^{1/g(x)}\right)\right)$$where Q(s,x)=\frac{\Gamma(s,x)}{\Gamma(s)} is the upper incomplete gamma function ... 3answers 135 views ### Multivariate functions whose value is independent of the order of the arguments Let r_1, r_2, \ldots, r_k be positive integers with or without repetition such that 1\le r_i \le n for i = 1, 2, \ldots, k. Let f be a continuous multivariate function with the property that ... 2answers 291 views ### Elliptic function with constant real part on the unit square diagonals? Consider the following even meromorphic doubly periodic function with poles at the gaussian integer lattice. H(z) = \prod_{n \in \mathbb{Z}} {1 \over{ 1 - {1 ... 3answers 706 views ### How to isolate f(x) in f(x+a)=f(x)+a\times g(x)? a \in \mathbb{R} f:\mathbb{R} \rightarrow \mathbb{R} g:\mathbb{R} \rightarrow \mathbb{R} For generic functions f and g, how isolate f(x) in the equation below? f(x+a)=f(x)+a\times ... 0answers 249 views ### High dimensional beta integral (question following the previous post) Hello, This post is a question following the previous post. In one dimensional case, we have$$ \int_0^x |y|^{1-\alpha} |x-y|^{1-\beta} d y = \frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)} ...
Hello, When I read Stein's book of Singular Integrals, at p. 118, there is an obvious mistake:  \int_{R^n} |x-y|^{-n+\alpha} ...