Quantum calculus

By J. Gazet. Mathematical Gazette, 2004

251 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/e96415e81e4feb2f1024d6582dfcd067ed34883c

Citations in the corpus

• A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, unknown): “Q-derivatives are part of so called quantum calculus [18, 19].”
• A Quantum Cluster Algebra of Kronecker Type and the Dual Canonical Basis (2010, unknown): “Note that some authors, for example [18], use a different notation for quantum integers.”
• Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers (2015, unknown): “For details on q-calculus and (p, q)-calculus, one can refer [15], [5, 12, 13], respectively.”
• CONTROLLABILITY, OBSERVABILITY, REALIZABILITY, AND STABILITY OF DYNAMIC LINEAR SYSTEMS (2009, unknown): “the quantum time scale used in quantum calculus [9]).”
• On integral representations of $q$-gamma and $q$-beta functions (2003, unknown): “Varchenko for sending corrections to the book [6], including the one mentioned above.”
• Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators (2016, unknown): “All of the previous concepts can be found in [11] and [17].”
• Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences (2012, unknown): “Basic properties of the two operators can be found in the book [29].”
• Nontrivial solutions for fractional q-difference boundary value problems (2010, unknown): “Basic properties of the two operators can be found in the book [11].”
• Exponential functionals of Levy processes (2005, unknown): “In order to specify the distribution of the exponential functional, it is quite convenient to use the so-called q -calculus (see, e.g. [31], [43], ...) which is associated with the basic hypergeometric series of Euler, Gauss, ...”
• The Convolution on Time Scales (2007, unknown): “We use the notation from [8], in particular [α]= [α]q = q α− 1 q− 1 , α∈R, [n]!= n ∏ k=1 [k], [ m n ] = [m]! [n]![m−n]! , m,n∈N0, (t− s)q = n−1 ∏ k=0 ( t− qks), t,s∈ T, n∈N0.”
• Multiple $q$-Zeta Values (2004, unknown): “Using th q-product rule forq-differentiation [14,22] in the form(Dqfg)(x) = g(x)(Dqf )(x) + f (qx)(Dqg)(x), one readily verifies that this definition of the q-shuffle ensures that equ tion”