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Covalency of M-N Bonds in Isomorphous Lanthanide and Actinide 5‑(2-Pyridyl)‑1<i>H</i>‑tetrazolate Complexes. [PDF]
JACS AuBai Z +6 more
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Cation Induced Structural Variation in Topochemically Modified Dion-Jacobson Perovskite Solid Solutions. [PDF]
MoleculesBhuvan R +5 more
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2014
In Chap.6 it is shown how power series techniques can be used to represent the solution of scalar first- and second-order differential equations. Special attention is paid to Legendre’s equation, Bessel’s equation, and the hypergeometric equation since these equations often occur in the applications.
Martin Hermann, Masoud Saravi
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In Chap.6 it is shown how power series techniques can be used to represent the solution of scalar first- and second-order differential equations. Special attention is paid to Legendre’s equation, Bessel’s equation, and the hypergeometric equation since these equations often occur in the applications.
Martin Hermann, Masoud Saravi
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Celestial Mechanics, 1970
A means of extending the radius of convergence of a power series solution of a system of differential equations is presented. It is essentially a change of the independent variable by means of a conformal mapping. Conditions on this change of variables which should yield a computational advantage are discussed.
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A means of extending the radius of convergence of a power series solution of a system of differential equations is presented. It is essentially a change of the independent variable by means of a conformal mapping. Conditions on this change of variables which should yield a computational advantage are discussed.
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2006
Abstract In this chapter, we investigate a special technique which provides solutions to a wide class of differential equations. Again, we concentrate on the homogeneous linear second-order equation where p 0, p 1, p 2 are continuous functions which we shall suppose throughout this chapter to have no common zeros.
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Abstract In this chapter, we investigate a special technique which provides solutions to a wide class of differential equations. Again, we concentrate on the homogeneous linear second-order equation where p 0, p 1, p 2 are continuous functions which we shall suppose throughout this chapter to have no common zeros.
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2019
Generally, second-order differential equations with variable coefficients cannot be solved in terms of the known functions. However, there is a fairly large class of differential equations whose solutions can be expressed either in terms of power series, or as simple combination of power series and elementary functions [1, 2, 3].
Ravi P. Agarwal +2 more
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Generally, second-order differential equations with variable coefficients cannot be solved in terms of the known functions. However, there is a fairly large class of differential equations whose solutions can be expressed either in terms of power series, or as simple combination of power series and elementary functions [1, 2, 3].
Ravi P. Agarwal +2 more
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2015
We have already seen in 3 that the solution of differential equations of constants coefficient depends on the solutions of the associated algebraic characteristic equation. There is no similar procedure for solving linear differential equation with variable coefficients.
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We have already seen in 3 that the solution of differential equations of constants coefficient depends on the solutions of the associated algebraic characteristic equation. There is no similar procedure for solving linear differential equation with variable coefficients.
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Power Series Solutions of ODEs and Frobenius Series
2001This chapter is devoted to the research of approximate solutions of nonlinear differential equations because for this kind of equation, it is exceptional to find the exact solutions. On the other hand, in the applications, it may be more useful to have an approximate solution with a simple form than an exact one with a very complex expression.
Addolorata Marasco, Antonio Romano
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