Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications by Lokenath Debnath, Bicheng Yang

“…Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. …”
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On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions by Muajebah Hidan, Mohamed Akel, Salah Mahmoud Boulaaras, Mohamed Abdalla

“…Recently, the applications and importance of integral transforms (or operators) with special functions and polynomials have received more attention in various fields like fractional analysis, survival analysis, physics, statistics, and engendering. …”
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Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion by Ndolane Sene

“…The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G-function. …”
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Certain Properties of Generalized M-Series under Generalized Fractional Integral Operators by D. L. Suthar, Fasil Gidaf, Mitku Andualem

“…Due to the general nature of the I-function and the generalized M-series, a number of results involving special functions can be achieved only by making appropriate values for the parameters.…”
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Exact Posterior distribution of risk ratio in the Kumaraswamy–Binomial model by Andrade, Jose A. A., Rathie, Pushpa

“…The results are based on special functions and we give exact expressions for the posterior density, moments, and cumulative distribution. …”
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On monomiality property of q-Gould-Hopper-Appell polynomials by Nusrat Raza, Mohammed Fadel, Subuhi Khan

“…Recently, in the theory of q-special functions, the extension of the monomiality concept to q-special polynomials is introduced. …”
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A New Class of Integrals Connected with Polynomials and Extended Generalized Mittag-Leffler Function by Nirmal Kumar Jangid, Sunil Joshi, Ekta Mittal

“…Further, we are also considering the integral formulae, which involve various special functions. Interesting special cases of the main results are also considered. …”
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k -Fractional Variants of Hermite-Mercer-Type Inequalities via s-Convexity with Applications by Saad Ihsan Butt, Jamshed Nasir, Shahid Qaisar, Khadijah M. Abualnaja

“…As an application viewpoint, certain estimates in respect of special functions and special means of real numbers are also illustrated to demonstrate the applicability and effectiveness of the suggested scheme.…”
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Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable by Najla M. Alarifi, Rabha W. Ibrahim

“…A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. …”
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Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments by Wei Li, Chang-Yuan Chen, Shi-Hai Dong

“…The present method can in principle be generalizable to the integrals involving other special functions. As an illustration we also study a typical Bessel integral with a complicated argument ∫0∞Jn(αx2+z2)/(x2+z2)nx2m+1dx.…”
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Harmonic analysis on the quantized Riemann sphere by Jaak Peetre, Genkai Zhang

“…In the course of the discussion many special functions (hypergeometric functions, orthogonal polynomials etc.) come up. …”
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A Domain-Specific Architecture for Elementary Function Evaluation by Anuroop Sharma, Christopher Kumar Anand

“…Our example instruction architecture (ISA) extension supports scalar and vector/SIMD implementations of table-based methods of calculating all common special functions, with the aim of improving throughput by (1) eliminating the need for tables in memory, (2) eliminating all branches for special cases, and (3) reducing the total number of instructions. …”
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Computation and interpretation of mean absolute deviations by cumulative distribution functions by Eugene Pinsky

“…Moreover, the CDFs are often expressed in terms of special functions, and indefinite integrals and sums for these functions are well known. …”
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Hermite–Hadamard–Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators by Noureddine Azzouz, Bouharket Benaissa, Hüseyin Budak, İzzettin Demir

“…Then, we give new identities of this type with special functions depending on ψ. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. …”
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Solutions of a Class of Multiplicatively Advanced Differential Equations II: Fourier Transforms by David W. Pravica, Njinasoa Randriampiry, Michael J. Spurr

“…In demonstrating this set of relations, the current study forges a systematic connection between the theory of MADEs and that of special functions. In a large subset of the general case, we introduce a new family of Schwartz wavelet MADE solutions Wμ,λt for μ and λ rational with λ>0. …”
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Quantum–Fractal–Fractional Operator in a Complex Domain by Adel A. Attiya, Rabha W. Ibrahim, Ali H. Hakami, Nak Eun Cho, Mansour F. Yassen

“…Some examples are considered, involving special functions like Bessel and generalized hypergeometric functions.…”
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Roles of Cells from the Arterial Vessel Wall in Atherosclerosis by Di Wang, Zhiyan Wang, Lili Zhang, Yi Wang

“…Additionally, the fibroblasts from the adventitia and adipocytes from perivascular adipose tissue have received considerable attention given their special functions that contribute to atherosclerosis. In addition, numerous types of cytokines produced by different cells from the arterial vessel wall, including endothelium-derived relaxing factors, endothelium-derived contracting factors, tumor necrosis factors, interleukin, adhesion molecules, interferon, and adventitium-derived relaxing factors, have been implicated in atherosclerosis. …”
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Quasinormal modes of three $$(2+1)$$ ( 2 + 1 ) -dimensional black holes in string theory, conformal gravity, and Hu–Sawicki F(R) theory via the Heun function by F. Naderi, A. Rezaei-Aghdam

“…Abstract We study the propagation of massless fermionic fields, implementing a family of special functions: Heun functions, in solving the wave equation in three three-dimensional backgrounds, including the BTZ black hole in string theory and Lifshitz black hole solutions in conformal gravity and Hu–Sawicki F(R) theory. …”
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Spatiotemporal distribution of rural multifunctionality and its influencing factors: a case study of the Liaoning Coastal Economic Belt, China by Yu Chen, Jun Wang

“…In China, rural areas have special functions that cannot be replaced by cities, such as residential carrying, agricultural and non-agricultural production, and ecological conservation. …”
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Comprehensive Analysis of Alpha-Parametric Set for the Calculation of Intersection Lengths of Radiological Ray Path in Siddon's Algorithm Used in 3D Image Reconstruction by Adem Polat

“…To prove our proposal, we performed lossy and lossless 3D image reconstruction (100×100×50) of a synthetic phantom. Using special functions that do not take into account the duplicate values and exclude them in the algorithm solved the stated problems (lossless reconstruction). …”
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