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Asymptotes --- Functions --- Approximation theory
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Differential equations --- Asymptotes. --- Numerical solutions.
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Differential equations --- Asymptotes --- Equations différentielles --- Asymptotes --- Numerical solutions --- Solutions numériques
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The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach - of Estrada, Kanwal and Vindas - is related
Asymptotic expansions. --- Asymptotic developments --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis
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Trajectories. --- Launching. --- Mission planning. --- Asymptotes. --- Targets. --- Deep space. --- Handbooks. --- Ballistic trajectories.
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Asymptotes --- Continuum mechanics --- Milieux continus, Mécanique des --- Milieux continus, Mécanique des --- Mathématiques --- Mathématiques --- Milieu continu --- Modélisation
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This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle's theory of terminants is then employed to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. Numerical results are used to illustrate that a complete asymptotic expansion can be made to agree with exact results for the generalised Euler-Jacobi series to any desired degree of accuracy. All researchers interested in the fascinating area of exponential asymptotics will find this a most valuable book.
Jacobi series. --- Asymptotic expansions. --- Asymptotic developments --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis --- Series, Jacobi --- Harmonic analysis --- Series
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Global theory of a second order linear ordinary differential equation with a polynomial coefficient
Differential equations --- Asymptotic expansions. --- Numerical solutions. --- Asymptotic developments --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis --- 517.91 Differential equations
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