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Results tagged with ca.classical-analysis-and-odes
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user 136807
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
3
votes
1
answer
239
views
Looking for bound in integral involving Legendre polynomial
I'm looking for an upper bound to the following integral or equivalent when $n$ leads to $ +\infty $ to the following expression
$$I_n:=\left|\int_{0}^1 \int_{0}^1 \frac{p_n(x) p_n(y)}{(1-xy)} dx dy …
- 417
2
votes
2
answers
155
views
question about equality series containing hypergeometric term and a simple term
I need a help about the following:
Maple gave that the following equality is true for n =1,2,3,4,5, $$ \sum_{h=0}^{\infty}\binom{n+h}{n}{_3}F_2\left( \substack{-h,n+1,n+1\\ 1,1}; x\right)= \frac{1}{x^ …
- 417