Мақаланы E-mail арқылы жіберу Infinite elliptic hypergeometric series: convergence and diffrence equations
- Авторлар: Krotkov D.I.1, Spiridonov V.P.2,1
-
Мекемелер:
- HSE University
- Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
- Шығарылым: Том 214, № 12 (2023)
- Беттер: 106-134
- Бөлім: Articles
- URL: https://bakhtiniada.ru/0368-8666/article/view/147930
- DOI: https://doi.org/10.4213/sm9874
- ID: 147930
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
We derive finite difference equations of infinite order for theta-hypergeometric series and investigate the space of their solutions. In general, such infinite series diverge, and we describe some constraints on the parameters when they do converge. In particular, we lift the Hardy-Littlewood criterion of the convergence of q-hypergeometric series for |q|=1, qn≠1, to the elliptic level and prove the convergence of infinite very-well poised elliptic hypergeometric r+1Vr-series for restricted values of q.
Негізгі сөздер
Авторлар туралы
Danil Krotkov
HSE University
Email: math-net2025_06@mi-ras.ru
Vyacheslav Spiridonov
Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics; HSE University
Хат алмасуға жауапты Автор.
Email: math-net2025_06@mi-ras.ru
Doctor of physico-mathematical sciences, no status
Әдебиет тізімі
- Р. Аски, Р. Рой, Дж. Эндрюс, Специальные функции, МЦНМО, М., 2013, 651 с.
- I. B. Frenkel, V. G. Turaev, “Elliptic solutions of the Yang–Baxter equation and modular hypergeometric functions”, The Arnold–Gelfand mathematical seminars, Birkhäuser Boston, Inc., Boston, MA, 1997, 171–204
- Дж. Гаспер, М. Рахман, Базисные гипергеометрические ряды, Мир, М., 1993, 349 с.
- S. Grepstad, L. Kaltenböck, M. Neumüller, “A positive lower bound for $lim inf_{Ntoinfty}prod_{r=1}^{N} |2sin pi rvarphi|$”, Proc. Amer. Math. Soc., 147:11 (2019), 4863–4876
- G. H. Hardy, J. E. Littlewood, “Notes on the theory of series (XXIV): a curious power-series”, Proc. Cambridge Philos. Soc., 42:2 (1946), 85–90
- D. S. Lubinsky, “The size of $(q; q)_n$ for $q$ on the unit circle”, J. Number Theory, 76:2 (1999), 217–247
- G. Petruska, “On the radius of convergence of $q$-series”, Indag. Math. (N.S.), 3:3 (1992), 353–364
- V. P. Spiridonov, “Theta hypergeometric series”, Asymptotic combinatorics with application to mathematical physics (St. Petersburg, 2001), NATO Sci. Ser. II Math. Phys. Chem., 77, Kluwer Acad. Publ., Dordrecht, 2002, 307–327
- V. P. Spiridonov, “An elliptic incarnation of the Bailey chain”, Int. Math. Res. Not. IMRN, 2002:37 (2002), 1945–1977
- V. P. Spiridonov, “Theta hypergeometric integrals”, Алгебра и анализ, 15:6 (2003), 161–215
- В. П. Спиридонов, “Очерки теории эллиптических гипергеометрических функций”, УМН, 63:3(381) (2008), 3–72
- A. Zhedanov, “Elliptic polynomials orthogonal on the unit circle with a dense point spectrum”, Ramanujan J., 19:3 (2009), 351–384
- A. Zhedanov, “Umbral “classical” polynomials”, J. Math. Anal. Appl., 420:2 (2014), 1354–1375
Қосымша файлдар
