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Reversion of power series by residues
Communications in Algebra, 1998The Grothendieck residue map is used to reverse power series in a characteristic-free manner. An operator theoretic method for reversing power series is linked to the Grothendieck residue method by local duality.
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Power-Series, Residues, Singularities
2020The sequence \(\{t_n\}_{n=0}^\infty \subseteq \mathbb C\) is said to converge absolutely if there is a β > 0 such that for each positive integer n we have \(\sum _{p=1}^{n}|t_p-t_{p-1}| \leq \beta \).
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Mathematics of the USSR-Sbornik, 1975
By means of a multidimensional analog of the theorem of logarithmic residues, representations are found for the implicit functions , , defined by the system of equations where , , , and as also for the function , , where and are holomorphic functions at , in the form of power series and certain function series.
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By means of a multidimensional analog of the theorem of logarithmic residues, representations are found for the implicit functions , , defined by the system of equations where , , , and as also for the function , , where and are holomorphic functions at , in the form of power series and certain function series.
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The Residual Power Series Method for Solving the Fractional Fuzzy Delay Differential Equation
2019In this paper, the fuzzy delay differential equation is expressed in fractional form, and the Residual Power Series Method (RPSM) is used to solve the equation. The delay differential equation indicates that in a system, the speed of the system is not only related to the current state of the system, but also depends on the historical trajectory until ...
Qiujuan Tong +2 more
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Residual Power Series Solution of Fractional bi-Hamiltonian Boussinesq System
2020In this paper, the residual power series method (RPSM) which is based on the generalized Taylor’s series formula has been used to investigate the approximated analytical solution for the fractional bi-Hamiltonian Boussinesq system. The solution of governing equation is calculated in the form of speedily convergent series.
Sachin Kumar, Baljinder Kour
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The Homological Properties of the Residue Rings of Skew Power Series
Pure Mathematics, 2020openaire +1 more source
Numerical Methods for Partial Differential Equations, 2021
Mahmut Modanli, Sadeq Taha Abdulazeez
exaly
Mahmut Modanli, Sadeq Taha Abdulazeez
exaly
Residual Power Series Method for Solving Linear Complex Differential Equations
Advances in Nonlinear Variational InequalitiesThis work uses the residual power series method (RPSM), primarily based on the general Taylor series formula with a residual error function, to offer solutions to instances of linear complex differential equations (LCDEs) as test problems. After finding approximate solutions to those problems, the current approach's findings have been compared with the
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Applications of the ARA-Residual Power Series Technique to Physical Phenomena
Applied Mathematics & Information Sciences, 2023openaire +1 more source