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Autor:
Finch, Steven
The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2411.16062
Autor:
Hang, Peng-Cheng, Luo, Min-Jie
For any $a\in\mathbb{C}$, the zeros of $\zeta(s)-a$, denoted by $\rho_a=\beta_a+i\gamma_a$, are called $a$-points of the Riemann zeta function $\zeta(s)$. In this paper, we reformulate some basic results about the $a$-points of $\zeta(s)$ shown by Ga
Externí odkaz:
http://arxiv.org/abs/2411.13255
Autor:
Nemes, Gergő
Simple asymptotic expansions for the Jacobi functions $P_\nu^{(\alpha, \beta)}(z)$ and $Q_\nu^{(\alpha, \beta)}(z)$ for large degree $\nu$, with fixed parameters $\alpha$ and $\beta$, are surprisingly rare in the literature, with only a few special c
Externí odkaz:
http://arxiv.org/abs/2411.10942
Autor:
Ameur, Yacin, Cronvall, Joakim
We consider a class of external potentials on the complex plane $\mathbb{C}$ for which the coincidence set to the obstacle problem contains a Jordan curve in the exterior of the droplet. We refer to this curve as a spectral outpost. We study the corr
Externí odkaz:
http://arxiv.org/abs/2411.10288
Autor:
Min, Chao, Fang, Pixin
We further study the orthogonal polynomials with respect to the generalized Airy weight based on the work of Clarkson and Jordaan [{\em J. Phys. A: Math. Theor.} {\bf 54} ({2021}) {185202}]. We prove the ladder operator equations and associated compa
Externí odkaz:
http://arxiv.org/abs/2411.07093
Autor:
Dixit, Atul, Kumar, Gaurav
Page 27 of Ramanujan's Lost Notebook contains a beautiful identity which not only gives, as a special case, a famous modular relation between the Rogers-Ramanujan functions $G(q)$ and $H(q)$ but also a relation between two fifth order mock theta func
Externí odkaz:
http://arxiv.org/abs/2411.06412
Autor:
Gaunt, Robert E., Ye, Zixin
We derive asymptotic expansions for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables. As a
Externí odkaz:
http://arxiv.org/abs/2411.03942
Autor:
Finch, Steven
N. G. de Bruijn (1958) studied the asymptotic expansion of iterates of sin$(x)$ with $0 < x \leq \pi/2$. Bencherif & Robin (1994) generalized this result to increasing analytic functions $f(x)$ with an attractive fixed point at 0 and $x > 0$ suitably
Externí odkaz:
http://arxiv.org/abs/2411.01591
Autor:
Hang, Peng-Cheng
Recently, Hang and Luo (2024) used an elementary approach to derive the leading asymptotic behavior of the Humbert function $\Psi_1[a,b;c,c';x,y]$ when $x\to\infty$ and $y\to +\infty$. In this paper, we give detailed asymptotic analyses of $\Psi_1$ w
Externí odkaz:
http://arxiv.org/abs/2410.21985
We examine the solution of the Benjamin-Ono Cauchy problem for rational initial data in three types of double-scaling limits in which the dispersion tends to zero while simultaneously the independent variables either approach a point on one of the tw
Externí odkaz:
http://arxiv.org/abs/2410.21581