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Mathematics : Recent Questions and Answers (Page 72)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Bessel functions in terms of the confluent hypergeometric function

I am familiar with the representation of the Bessel functions as $$J_m(x) = left(frac{x}{2}right)^m sum_{k = 0}^{infty} frac{(-1)^k}{k! (k + m)!} left(frac{x}{2}right)^{2k},$$ for some integer $m$. Now, I...

Asked on 11/21/2021 by user785957

1 answer

Prove that $text{tr} (phi otimes psi) = text {tr} phi text {tr} psi $.

Let $E,F$ be two vector spaces of dimension $n$ and $m$ respectively and let $phi : E rightarrow E$,$psi : F rightarrow F $...

Asked on 11/21/2021

2 answer

Why do we consider the zeroes of the expression when solving rational inequalities?

When finding the solution set of rational inequalities (of the form $ {x-3over x+2} geq 0 $ etc.) , why do we consider the "zeroes" of the expression. So...

Asked on 11/21/2021 by Shaheer ziya

2 answer

Is the theory of sheaves a first order theory?

Is the theory of sheaves a first order theory?How should I check if a theory is first order or not?...

Asked on 11/21/2021 by user297564

0 answer

Finding $P[X+Y > 1, X > 1]$

I'm trying to solve the following problem: i have two independent exponentially distributed r.v. $X$ and $Y$ both with $lambda = 1$. I want to know the...

Asked on 11/21/2021 by damianodamiano

1 answer

What is a 2-fraction?

I am working with a 4-term recurrence relation coming from the application of the Frobenius method on a ODE, in particular I am studying the convergence of the resulting series....

Asked on 11/21/2021

0 answer

Need some help with solving this integral.....

I have to solve the following integral as part of another bigger expression:$$int_{A}^{1}{x over 1 - x},(x - A)^{-varepsilon} ln(x)left{1+2left[ln(x) - {1 + x over x},ln(1 -...

Asked on 11/21/2021 by PhysicsLab1

0 answer

How to evaluate/simplify integration with 4 parts?

How might I evaluate the following indefinite integral? $$int k , x^a ,(1-x)^b ,(x-y)^c , (1-x+y)^d ,,dx$$ The aim is to get a function of $y$ once I...

Asked on 11/21/2021

0 answer

Laplacian coupled with another equation over a two-dimensional rectangular region

I have the two-dimensional Laplacian $(nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $xin[0,L], yin[0,l]$. On manipulating the second equation (which I have described in...

Asked on 11/21/2021

0 answer

Some Combinatorics and Some Prime Numbers

Problem statement: Let $U={1,2,...n}$ and $S$ be the set of all permutations of the elements of $U$. For any $f in S$ let $I(f)$ denotes...

Asked on 11/21/2021 by Shubhrajit Bhattacharya

3 answer

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