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Relevant bibliographies by topics / Q-series expansion

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Academic literature on the topic 'Q-series expansion'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Q-series expansion"

1

McIntosh, Richard J. "Asymptotic Transformations of q-Series." Canadian Journal of Mathematics 50, no. 2 (1998): 412–25. http://dx.doi.org/10.4153/cjm-1998-022-x.

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AbstractFor the q–series we construct a companion q–series such that the asymptotic expansions of their logarithms as q → 1– differ only in the dominant few terms. The asymptotic expansion of their quotient then has a simple closed form; this gives rise to a new q–hypergeometric identity. We give an asymptotic expansion of a general class of q–series containing some of Ramanujan's mock theta functions and Selberg's identities.

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Annaby, M. H., Z. S. Mansour, and I. A. Soliman. "q-Titchmarsh-Weyl theory: series expansion." Nagoya Mathematical Journal 205 (March 2012): 67–118. http://dx.doi.org/10.1215/00277630-1543787.

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AbstractWe establish a q-Titchmarsh-Weyl theory for singular q-Sturm-Liouville problems. We define q-limit-point and q-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jackson q-Bessel functions is given. This example leads to the completeness of a wide class of q-cylindrical functions.

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Annaby, M. H., Z. S. Mansour, and I. A. Soliman. "q-Titchmarsh-Weyl theory: series expansion." Nagoya Mathematical Journal 205 (March 2012): 67–118. http://dx.doi.org/10.1017/s002776300001045x.

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AbstractWe establish aq-Titchmarsh-Weyl theory for singularq-Sturm-Liouville problems. We defineq-limit-point andq-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jacksonq-Bessel functions is given. This example leads to the completeness of a wide class ofq-cylindrical functions.

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Al-Towailb, Maryam, and Zeinab S. I. Mansour. "A q-Analog of the Class of Completely Convex Functions and Lidstone Series." Axioms 12, no. 5 (2023): 412. http://dx.doi.org/10.3390/axioms12050412.

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This paper introduces a q-analog of the class of completely convex functions. We prove specific properties, including that q-completely convex functions have convergent q-Lidstone series expansions. We also provide a sufficient and necessary condition for a real function to have an absolutely convergent q-Lidstone series expansion.

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LIU, ZHI-GUO. "ON THE q-DERIVATIVE AND q-SERIES EXPANSIONS." International Journal of Number Theory 09, no. 08 (2013): 2069–89. http://dx.doi.org/10.1142/s1793042113500759.

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Using a general q-series expansion, we derive some nontrivial q-formulas involving many infinite products. A multitude of Hecke-type series identities are derived. Some general formulas for sums of any number of squares are given. A new representation for the generating function for sums of three triangular numbers is derived, which is slightly different from that of Andrews, also implies the famous result of Gauss where every integer is the sum of three triangular numbers.

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Banerjee, Shubho, and Blake Wilkerson. "Asymptotic expansions of Lambert series and related q-series." International Journal of Number Theory 13, no. 08 (2017): 2097–113. http://dx.doi.org/10.1142/s1793042117501135.

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We study the Lambert series [Formula: see text], for all [Formula: see text]. We obtain the complete asymptotic expansion of [Formula: see text] near [Formula: see text]. Our analysis of the Lambert series yields the asymptotic forms for several related [Formula: see text]-series: the [Formula: see text]-gamma and [Formula: see text]-polygamma functions, the [Formula: see text]-Pochhammer symbol and the Jacobi theta functions. Some typical results include [Formula: see text] and [Formula: see text], with relative errors of order [Formula: see text] and [Formula: see text] respectively.

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Al-Towailb, Maryam, and Zeinab Mansour. "Conditional Expanding of Functions by q-Lidstone Series." Axioms 12, no. 1 (2022): 22. http://dx.doi.org/10.3390/axioms12010022.

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This paper characterizes those functions given by convergent q-Lidstone series expansion. We give the necessary and sufficient conditions so that the entire function f(z) has such an expansion, in which case convergence is uniform on compact sets.

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8

Ahmad, Naeem, and Waseem Ahmad Khan. "Insights into New Generalization of q-Legendre-Based Appell Polynomials: Properties and Quasi Monomiality." Mathematics 13, no. 6 (2025): 955. https://doi.org/10.3390/math13060955.

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In this paper, by using the zeroth-order q-Tricomi functions, the theory of three-variable q-Legendre-based Appell polynomials is introduced. These polynomials are studied by means of generating functions, series expansions, and determinant representation. Further, by utilizing the concepts of q-quasi-monomiality, these polynomials are examined as several q-quasi-monomial and operational representations; the q-differential equations for the three-variable q-Legendre-based Appell polynomials were obtained. In addition, we established a new generalization of three-variable q-Legendre-Hermite-App

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Charalambides, Charalambos A. "A Class of Power Series q-Distributions." Mathematics 12, no. 5 (2024): 712. http://dx.doi.org/10.3390/math12050712.

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A class of power series q-distributions, generated by considering a q-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q-factorial moments are obtained in terms of q-derivatives of its series (parametric) function. Also, it is shown that the convolution of power series q-distributions is also a power series q-distribution. Furthermore, the q-Poisson (Heine and Euler), q-binomial of the first kind, negative q-binomial of the second kind, and q-logarithmic distributions are shown to be members of this class of distributions and their q-factorial moments a

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He, Bing, and Suzhen Wen. "Some expansion formulas for q-series and their applications." Journal of Combinatorial Theory, Series A 209 (January 2025): 105941. http://dx.doi.org/10.1016/j.jcta.2024.105941.

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Book chapters on the topic "Q-series expansion"

1

Gasper, George. "Bibasic Summation, Transformation and Expansion Formulas, q-Analogues of Clausen’s Formula, and Nonnegative Basic Hypergeometric Series." In q-Series and Partitions. Springer US, 1989. http://dx.doi.org/10.1007/978-1-4684-0637-5_2.

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Andrews, George E., Arnold Knopfmacher, Peter Paule, and Burkhard Zimmermann. "Engel Expansions of q-Series by Computer Algebra." In Developments in Mathematics. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0257-5_3.

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Hirschhorn, Michael D. "The Series Expansion of the Rogers–Ramanujan Continued Fraction and Its Reciprocal." In The Power of q. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57762-3_16.

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Caraiani, Ana, Ellen Eischen, Jessica Fintzen, Elena Mantovan, and Ila Varma. "p-Adic q-Expansion Principles on Unitary Shimura Varieties." In Association for Women in Mathematics Series. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30976-7_7.

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Hirschhorn, Michael D. "The Series Expansion of the Ramanujan–Göllnitz–Gordon Continued Fraction and Its Reciprocal." In The Power of q. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57762-3_18.

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Andrews, George E. "Symmetric Expansions of Very Well-Poised Basic Hypergeometric Series." In Frontiers in Orthogonal Polynomials and q-Series. WORLD SCIENTIFIC, 2018. http://dx.doi.org/10.1142/9789813228887_0003.

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Conference papers on the topic "Q-series expansion"

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Hen, Itay. "Q-CASA Invited Speaker Simulating Hamiltonian Dynamics with the Off-diagonal Series Expansion." In 2023 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW). IEEE, 2023. http://dx.doi.org/10.1109/ipdpsw59300.2023.00086.

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Sharma, Kal Renganathan. "Mesoscopic Heat Conduction and Onset of Periodicity." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47391.

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Mesoscopic approach deals with study that considers temporal fluctuations which is often averaged out in a macroscopic approach without going into the molecular or microscopic approach. Transient heat conduction cannot be fully described by Fourier representation. The non-Fourier effects or finite speed of heat propagation effect is accounted for by some investigators using the Cattaneo and Vernotte non-Fourier heat conduction equation: q=−k∂T/∂x−τr∂q/∂t(1) A generalized expression to account for the non-Fourier or thermal inertia effects suggested by Sharma (5) as: q=−k∂T/∂x−τr∂q/∂t−τr2/2!∂2q

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Bowers, Mark S., and Stephen E. Moody. "Spatial and temporal behavior of gain-switched Ti:Al2O3 unstable resonator lasers." In OSA Annual Meeting. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.thmm37.

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Efficient high energy Ti:Al2O3 lasers are currently of interest as coherent sources for a variety of applications, such as laser atmospheric sensing. Furthermore, the output of such lasers can be converted to visible and UV wavelengths through frequency conversion processes. We report here on a novel method for modeling these lasers. The exact cavity equations of motion coupled with realistic time-dependent laser kinetics are solved numerically to obtain the 2-D radially-symmetric time-dependent electric field inside the optical cavity of an injection-seeded Ti:Al2O3 laser with an unstable res

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