I’m new with Maple and want to define a recurrence relation. I want to 1) have Maple solve it to the explicit formula 2)have Maple output a few evaluations of it for various values of n For example if I have $a_n=2a_{n-1}+3a_{n-2}$ with $a_0=1$ and $a_1=2$ how would I use Maple to solve for an […]

I try to prove several hard combinatorial identities. One of them is following \begin{align*} \sum_{s=0}^{\min\{k,n-1\}} \sum_{i=0}^{k-s} (-1)^{i} {2n+k-i-1 \choose k-s-i} {i-n \choose s} {n+i-1 \choose i} {n+k-s-1 \choose k} =\\ =\sum_{j=0}^{[\frac k2]} \sum_{i=0}^{min\{j, n-1\}}{ n-1 \choose i}^2 {{2n+j-i-2} \choose j-i} { n+k-2j-1 \choose n-1} .\text{ ($n,k$ are nonnegative integer)} \end{align*} Using the identity of Le-Jen […]

I would like to evaluate the following integral: $$\int_{1}^{\infty} x^{-5/3} \cos\left((x-1) \tau\right) dx$$ I get the Integral by Maple and it gives the Lommel function. After that, I will search an asymptotic as $\tau$ goes to $\infty$.

Intereting Posts

How do we show that $\int_{0}^{1}{\ln^k(x)\over x}\ln\left(1-\sqrt{x}\right)\mathrm dx=(-n)^{k+1}k!\zeta(k+2)?$
Obtaining a deeper understanding of lower level Mathematics
Infinitely many primes of the form $8n+1$
Find the recurrence relation for the number of bit strings that contain the string $01$.
What seemingly innocuous results in mathematics require advanced proofs?
How to find unique multisets of n naturals of a given domain and their numbers?
Why is the sequential closure not sequentially closed?
Possibilities of an action of $S^1$ on a disk.
Evaluate $\int_0^\infty\frac {\sin^4(x)} {x^4} \operatorname dx$
Show that the number 9 divides the number $ m$ if and only if the sum of the digits of the number $ m $ is divisible by 9.
What's the proof that the Euler totient function is multiplicative?
Advantages of IMO students in Mathematical Research
What does $\lim\limits_{x\to\pi/6}\frac{1-\sqrt{3}\tan x}{\pi-6x}$ evaluate to?
How to solve the Riccati's differential equation
Logic and set theory textbook for high school