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pro vyhledávání: '"q-Difference equations"'
We prove a connection formula for the basic hypergeomtric function ${}_n\varphi_{n-1}\left( a_1,...,a_{n-1},0; b_1,...,b_{n-1} ; q, z\right)$ by using the $q$-Borel resummation. As an application, we compute $q$-Stokes matrices of a special confluent
Externí odkaz:
http://arxiv.org/abs/2412.02281
The differential nature of solutions of linear difference equations over the projective line was recently elucidated. In contrast, little is known about the differential nature of solutions of linear difference equations over elliptic curves. In the
Externí odkaz:
http://arxiv.org/abs/2409.10092
Autor:
Del Monte, Fabrizio, Longhi, Pietro
This paper studies the space of monodromy data of second order $q$-difference equations through the framework of WKB analysis. We compute the connection matrices associated to the Stokes phenomenon of WKB wavefunctions and develop a general framework
Externí odkaz:
http://arxiv.org/abs/2406.00175
Autor:
Korhonen, Risto, Zhang, Yueyang
We consider the first order $q$-difference equation \begin{equation}\tag{\dag} f(qz)^n=R(z,f), \end{equation} where $q\not=0,1$ is a constant and $R(z,f)$ is rational in both arguments. When $|q|\not=1$, we show that, if $(\dag)$ has a zero order tra
Externí odkaz:
http://arxiv.org/abs/2405.03936
Autor:
Cano, J., Ayuso, P. Fortuny
Given a differential or $q$-difference equation $P$ of order $n$, we prove that the set of exponents of a generalized power series solution has its rational rank bounded by the rational rank of the support of $P$ plus $n$. We also prove that when the
Externí odkaz:
http://arxiv.org/abs/2406.06115
Autor:
Smirnov, Andrey
In this note we consider a class of $q$-hypergeometric equations describing the quantum difference equation for the cotangent bundle over projective space $X=T^{*}\mathbb{P}^n$ . We show that over $\mathbb{Q}_p$ these equations are equipped with the
Externí odkaz:
http://arxiv.org/abs/2406.00206
Akademický článek
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Akademický článek
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Autor:
Etemad, Sina1 (AUTHOR) sina.etemad@azaruniv.ac.ir, Stamova, Ivanka2 (AUTHOR) ivanka.stamova@utsa.edu, Ntouyas, Sotiris K.3 (AUTHOR) sntouyas@uoi.gr, Tariboon, Jessada4 (AUTHOR) ivanka.stamova@utsa.edu
Publikováno v:
Fractal & Fractional. Aug2024, Vol. 8 Issue 8, p443. 23p.
Exponentially-improved asymptotics for $q$-difference equations: ${}_2\phi_0$ and $q{\rm P}_{\rm I}$
Autor:
Joshi, Nalini, Daalhuis, Adri Olde
Usually when solving differential or difference equations via series solutions one encounters divergent series in which the coefficients grow like a factorial. Surprisingly, in the $q$-world the $n$th coefficient is often of the size $q^{-\frac12 n(n
Externí odkaz:
http://arxiv.org/abs/2403.02196