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I need to solve the following equation $$-\frac{\partial S(x,y,t)}{\partial t}=ax^2+bx\frac{\partial S(x,y,t)}{\partial x}+c\Big[\frac{\partial S(x,y,t)}{\partial ... 1answer 159 views ### Representation for increasing function on unit square Do you know any result concerning the representation of functions f : [0,1] \to [0,1] continuous and increasing (with f(0)=0,f(1)=1)) as convex combinations of a family of particular functions? ... 1answer 270 views ### Meaning of \alpha in Laguerre polynomials I found that generalized Laguerre polynomials are:$$ L_n^{\alpha} (x) = \sum_{i=0}^n (-1)^i {n+\alpha \choose n-i} \frac{x^i}{i!}.$$However, I wonder what is the meaning of \alpha in this ... 1answer 215 views ### prove equality with integral and series I am stuck on one question with integral. Help me please to show that with n=1 the following is true$$ ...
Let $n$ be half an odd integer, say $n=k+1/2, k \in Z$. Let $q\geq 1$. I would like to calculate (or approximate) the following integral  \int_0^{\infty}\left(\sqrt{\frac{\pi}{2}}\cdot 1\cdot 3\cdot ...