“…In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. …”
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“…The power series solution agrees well with the exact analytical solution when the material varies along its thickness following the same exponential function. …”
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“…Well-known book provides a clear, concise review of complex numbers and their geometric representation; linear functions and circular transformations; sets, sequences, and power series; analytic functions and conformal mapping; and elementary functions. 1952 edition.…”
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“…RESULTS: Group invariant solutions and power series solutions were constructed and three conserved vectors for the system were derived. …”
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“…With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers–Moyal coefficients. …”
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“…Pauli writes about the connection of renormalization with power series expansion. He makes some remarks on the difficulties of meson theories and on mathematical formulation of fundamental laws of nature. …”
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“…He also writes of a solution of the Schrödinger equation in the present theory of holes by a power-series of e$^{2}$(h.c.).…”
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“…The quantitative relationship between the power series of the projection and the nth moment of the linear attenuation coefficient spectrum of the phantom was also determined. …”
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“…Ordinary Differential EquationsDEFINITIONS LINEAR DIFFERENTIAL EQUATIONS OF FIRST ORDER LINEAR INDEPENDENCE AND THE WRONSKIAN LINEAR HOMOGENEOUS DIFFERENTIAL EQUATION OF ORDER N WITH CONSTANT COEFFICIENTS EULER'S EQUATION PARTICULAR SOLUTIONS BY METHOD OF UNDETERMINED COEFFICIENTS PARTICULAR SOLUTIONS BY THE METHOD OF VARIATIONS OF PARAMETERS ABEL'S FORMULA FOR THE WRONSKIAN INITIAL VALUE PROBLEMSSeries Solutions of Ordinary Differential EquationsINTRODUCTION POWER SERIES SOLUTIONS CLASSIFICATION…”
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“…We determine the Toda potential in each case and examine the free field realization of the corresponding solutions, using infinite power series expansions. The Atiyah-Hitchin metric exhibits some unusual features attributed to topological properties of the group of area preserving diffeomorphisms. …”
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“…In this paper, the solution methodology of higher-order linear fractional partial deferential equations (FPDEs) as mentioned in eqs (1) and (2) below in Caputo definition relies on a new analytical method which is called the Laplace-residual power series method (L-RPSM). The main idea of our proposed technique is to convert the original FPDE in Laplace space, and then apply the residual power series method (RPSM) by using the concept of limit to obtain the solution. …”
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“…Nevertheless, we provide evidence that this theory can be understood in a 1/N expansion since our correlators look like free-field correlators corrected by a power series in 1/N . However, on examining these corrections we find that the four point function of the two bulk scalar fields is corrected at leading order in 1/N through the contribution of one of the additional light operators in an OPE channel. …”
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“…The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. …”
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“…Pointwise and uniform convergence of series of functions, power series, treatment of trigonometric and exponential functions in terms of series are discussed. …”
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“…Finally, we solve the differential equations in terms of generalized power series and provide high-precision values in different regions of phase space which can be used as boundary conditions for subsequent evaluations.…”
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“…Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. …”
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“…Part 2 looks into the practical aspects of programming languages, including in lists and power series, fractal curves, and minimal surfaces.This book will prove useful to mathematicians and computer scientists.…”
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“…Topics include the solution of second-order differential equations in terms of power series; gamma and beta functions; Legendre polynomials and functions; Bessel functions; Hermite, Laguerre, and Chebyshev polynomials; Gegenbauer and Jacobi polynomials; and hypergeometric and other special functions. …”
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“…The book first offers information on the properties of Z, including symmetry properties, values for special arguments, power series, asymptotic expansion, and differential equation characterization. …”
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