“…On the basis of run semantics and breadth-first algebraic semantics, the algebraic characterizations for a classes of formal power series over complete strong bimonoids are investigated in this paper. …”
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“…In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. …”
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“…A new generalized class of distributions called the Lindley-Burr XII Power Series (LBXIIPS) distribution is proposed and explored. …”
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“…A new distribution, the type II exponentiated half logistic-odd Burr X-G power series (TII-EHL-OBX-GPS), is introduced in this study. …”
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“…Also, a graph is plotted to analyze the variations in unsteady temperature gradient using the finite difference method (FDM) and generalized residual power series method (GRPSM). The major result of this investigation unveils that as the convection-conduction parameter scale upsurges, the distribution of temperature in the fin diminishes. …”
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“…The considered methodology for finding the fuzzy solutions relies on converting the target equations into two fractional crisp systems in terms of ρ-cut representations. The residual power series therefore gives solutions for the converted systems by combining fractional residual functions and fractional Taylor expansions to obtain values of the coefficients of the fractional power series. …”
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“…<br><br>The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. …”
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“…The solution is found as a fractional power series. The coefficients of that power series are related to the Euler polynomials and Euler numbers as well as to the sequence of Euler’s fractional numbers recently introduced. …”
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“…In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function [Formula: see text] and a new criterion for the monotonicity of the quotient of two power series.…”
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“…Number Systems The Real Numbers The Complex Numbers Sequences Convergence of Sequences Subsequences Limsup and Liminf Some Special Sequences Series of Numbers Convergence of Series Elementary Convergence Tests Advanced Convergence Tests Some Special Series Operations on Series Basic Topology Open and Closed Sets Further Properties of Open and Closed Sets Compact Sets The Cantor SetConnected and Disconnected Sets Perfect Sets Limits and Continuity of Functions Basic Properties of the Limit of a Function Continuous Functions Topological Properties and Continuity Classifying Discontinuities and Monotonicity Differentiation of Functions The Concept of Derivative The Mean Value Theorem and Applications More on the Theory of Differentiation The Integral Partitions and the Concept of Integral Properties of the Riemann IntegralSequences and Series of Functions Convergence of a Sequence of Functions More on Uniform Convergence Series of Functions The Weierstrass Approximation Theorem Elementary Transcendental Functions Power Series More on Power Series: Convergence Issues The Exponential and Trigonometric Functions Logarithms and Powers of Real Numbers Appendix I: Elementary Number Systems Appendix II: Logic and Set Theory Table of Notation Glossary Bibliography Index.…”
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“…This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). …”
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“…In theory, an entire function can be uniquely determined by its values in a small region, using, for example, power series expansions. Power series expansions require evaluation of all orders of derivatives of a function, which is an impossible task if the function is discretely sampled. …”
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“…By using the residual power series method, we obtain a fractional power series approximation of the analytic solution. …”
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“…This book comprises of the topics on Differential Equation, Laplace Transform, Uniform Convergence of Sequence and Series of Functions, Power Series and Fourier Series for the students.…”
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“…For the spatial dependence of the nPDFs we used a power series ansatz in the nuclear thickness function $T_A$. …”
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“…Pauli gives details of his discussion with Dyson about his definition of renormalization through power-series.…”
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