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Results tagged with polynomials
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user 46744
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
5
votes
Are these two new ways of representing odd zeta values as integrals known?
{\pi^{2n-1}}\left( 2-2^{-2n} \right)\zeta(2n+1)
\end{equation}
where $E_n(x)$ are the Euler polynomials. … This result gives an explicit representation of the polynomials derived in my previous answer. …
- 791
1
vote
Accepted
Integral with Bessel function and hypergeometric function ${}_2F_2$: explicit expression for...
polynomials can be expressed using analogous of the Lommel polynomials for the modified Bessel functions. … $r_k^0(x)$ and $s_k^0(x)$ are given either in terms of the Lommel polynomials or explicitly. …
- 791
9
votes
Are these two new ways of representing odd zeta values as integrals known?
One may characterize more precisely the family of these polynomials. … cos\pi y/2}Q(y)\,dy=\left( -1 \right)^p8\left( 2^{2p+3}-1 \right)\frac{\zeta(2p+3)}{\pi^{2p+3}}
\end{equation}
The condition reads
\begin{equation}
Q(y)+Q(-y)=2g_p(y)
\end{equation}
The first polynomials …
- 791