Two Computational Strategies for the Approximate Solution of the Nonlinear Gas Dynamic Equations by Muhammad Nadeem, Mouad M. H. Ali

“…The implementation of this numerical scheme is straightforward and produces the results directly without any assumptions and hypothesis in the recurrence relation. Sawi transform (ST) has an advantage of reducing the computational work and the error of estimated results towards the precise solution. …”
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Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift by Gemechis File, Y. N. Reddy

“…Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. …”
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Degenerate Poly-Lah-Bell Polynomials and Numbers by Taekyun Kim, Hye Kyung Kim

“…We give their explicit expression, Dobinski-like formulas, and recurrence relation. In addition, we obtain various algebraic identities including Lah numbers, the degenerate Stirling numbers of the first and second kind, the degenerate poly-Bell polynomials, the degenerate poly-Bernoulli numbers, and the degenerate poly-Genocchi numbers.…”
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering by Taekyun Kim, Dae San Kim, Hye Kyung Kim

“…In particular, we obtain two expressions for the generating function of the degenerate r-Bell polynomials in z2, and a recurrence relation and Dobinski-like formula for the degenerate r-Bell numbers. …”
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On the Solutions of Okubo-Type Systems by Galina Filipuk, Alberto Lastra

“…It is also expressed as a power series about the origin with coefficients satisfying certain recurrence relation. This extends the results in (W. Balser, C. …”
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Simulated annealing on uncorrelated energy landscapes by Ben Goertzel, Malwane Ananda

“…This paper studies the effectiveness of simulated annealing as a strategy for optimizing uncorrelated functions. A recurrence relation expressing the effectiveness of the algorithm in terms of the function G is derived. …”
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Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme by Muhammad Nadeem, Hanan A. Wahash

“…Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. …”
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Success Run Waiting Times and Fuss-Catalan Numbers by S. J. Dilworth, S. R. Mane

“…We present power series expressions for all the roots of the auxiliary equation of the recurrence relation for the distribution of the waiting time for the first run of k consecutive successes in a sequence of independent Bernoulli trials, that is, the geometric distribution of order k. …”
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Building some symmetric Laguerre-Hahn functionals of class two at most through the sum of symmetric functionals as pseudofunctions with a Dirac measure at origin by M. Sghaier, J. Alaya

“…We explicitly give the coefficients of the second-order recurrence relation, the structure relation of the orthogonal sequence associated with u, and the class of the linear form u knowing that of v. …”
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A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems by Yasser Mohamed Hamada

“…These coefficients can be determined by equating the high derivatives of the Chebyshev series with those obtained by the given system. A new recurrence relation is introduced to determine the series coefficients. …”
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New extensions of associated Laguerre polynomials by Ahmed Ali Al-Gonah

“…Some integral representations, recurrence relations, generating functions and summation formulae are obtained for these new extended Laguerre polynomials.…”
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Some Results on the Extended Hypergeometric Matrix Functions and Related Functions by Mohamed Abdalla, Sahar Ahmed Idris, Ibrahim Mekawy

“…The current results for these functions include integral representations, transformation formula, recurrence relations, and integral transforms.…”
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Binomial Transforms of the Padovan and Perrin Matrix Sequences by Nazmiye Yilmaz, Necati Taskara

“…Also, the Binet formulas, summations, and generating functions of these transforms are found by recurrence relations. Finally, we illustrate the relations between these transforms by deriving new formulas.…”
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A Note on Generalized <i>k</i>-Order F&L Hybrinomials by Süleyman Aydınyüz, Gül Karadeniz Gözeri

“…A key aspect of our research is the establishment of the recurrence relations for generalized <i>k</i>-order F&L hybrinomials. …”
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The K Extended Laguerre Polynomials Involving Aαr,n,kxFr r,r>2 by Adnan Khan, M. Haris Mateen, Ali Akgül, Md. Shajib Ali

“…Additionally, we describe the K generating function, K recurrence relations, and KS Rodrigues formula.…”
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The Hermite polynomials and the Bessel functions from a general point of view by G. Dattoli, H. M. Srivastava, D. Sacchetti

“…We study their relevant recurrence relations and show that they satisfy differential-difference equations which are isospectral to those of the ordinary case. …”
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Some Identities of Fully Degenerate Dowling Polynomials and Numbers by Lingling Luo, Yuankui Ma, Wencong Liu, Taekyun Kim

“…We also obtain the generating functions, expressions, and recurrence relations for the fully degenerate Dowling polynomials and the fully degenerate Bell polynomials and other special polynomials and numbers.…”
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The Hyperspherical Functions of a Derivative by Nenad Cakic, Duško Letic, Branko Davidovic

“…We present the results of theoretical research of the generalized hypersherical function (HS) by generalizing two known functions related to the sphere hypersurface and hypervolume and the recurrent relation between them. By introducing two-dimensional degrees of freedom k and n (and the third, radius r), we develop the derivative functions for all three arguments and the possibilities of their use. …”
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Orthogonal Polynomials of Compact Simple Lie Groups by Maryna Nesterenko, Jiří Patera, Agnieszka Tereszkiewicz

“…The obtained not Laurent-type polynomials are equivalent to the partial cases of the Macdonald symmetric polynomials. Recurrence relations are shown for the Lie groups of types A1, A2, A3, C2, C3, G2, and B3 together with lowest polynomials.…”
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Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces by Abhimanyu Kumar, Dharmendra K. Gupta, Eulalia Martínez, Sukhjit Singh

“…The semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces. The recurrence relations are derived under weaker conditions on the operator. …”
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