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Showing 1 to 20 of 78 for “"Power series"”.
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Locally Power Series Algebras
Made available in DSpace on 2014-12-14T13:09:42Z (GMT). No. of bitstreams: 1 8004212.pdf: 3200460 bytes, checksum: 6dfe6e6782cbbf894c83c57fd9f56972 (MD5) Previous issue date: 1979
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Transcendence degree in power series rings
Let D[[X]] be the ring of formal power series over the commutative integral domain D. Gilmer has shown that if K is the quotient field of D, then D[[X]] and K[[X]] have the same quotient field if and only if K[[X]] ~ D[[X]]D_(O). Further, if a is any nonzero element of D, Sheldon has shown that …
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Power Series Solutions to Ordinary Differential Equations
… reader will be made aware of methods for finding power series solutions to ordinary differential equations. In the case that a solution to a differential equation may not be expressed in terms of elementary functions, it is practical to obtain a solution in the form of an infinite series, since …
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Zeros of partial sums of power series
A classical result of Jentzsch states that, for a power series with radius of convergence one, every point on the unit circle is a limit point of zeros of partial sums of the power series. In this thesis, the relationship between the properties of the function and the behavior of the zeros of its …
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Extremal problems for polynomials and power series
Thesis (Ph.D.) Massachusetts Institute of Technology. Dept. of Mathematics, 1952.
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Extremal problems for polynomials and power series
Thesis (M.S.) Massachusetts Institute of Technology. Dept. of Mathematics, 1951.
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Rational Iterated Integrals and Formal Power Series Connections
Made available in DSpace on 2014-12-14T13:09:34Z (GMT). No. of bitstreams: 1 7726655.pdf: 2020039 bytes, checksum: f8cbed2d1f423d2078db61e9b1de9ac5 (MD5) Previous issue date: 1977
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"The ""KUTTER"" formula as an infinite power series"
Made available in DSpace on 2017-11-30T22:11:14Z (GMT). No. of bitstreams: 2 6461143.pdf: 1006094 bytes, checksum: d433f27c95802bac26c75e71c4540b95 (MD5) license.txt: 4813 bytes, checksum: 715c4321821a960fa1a1e91d2ac7ebce (MD5) Previous issue date: 1939
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Efficient Algorithms and Parallel Implementations for Power Series Multiplication
Power series play an important role in solving differential equations and approximating functions. A key operation in manipulating power series is their multiplication. Power series multiplication algorithms working based on a prescribed precision, say $n$ (where $n$ is a natural number), take the …
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Dynamical statistics for power series and polynomials with restricted coefficients
… these fractals are closely related to power series with all coefficients equal to ±1. Motivated by the Julia–Mandelbrot correspondence, we construct a natural measure in the parameter space satisfying analogous properties for this family. Viewing the natural measure as an average …
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Some Inequalities Concerning Power Series and Their Interaction With Univalent Function Theory
Power series are fundamental in the study of Geometric Function Theory. In fact, they constitute a major part in Complex Analysis. The purpose of this dissertation is to employ analytic functions defined by power series in two different directions. The first of these discussed in Part I, mainly …
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Families of ideals in the ring of power series in two variables.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1970
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Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms
… Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms. We prove his formulas for the coefficients of 1/$E\sb4, E\sb4/E\sb6$ and other functions involving the Eisenstein series $E\sb4, E\sb6$ and $E\sbsp{2}{*}$. These formulas are stated, without proof, …
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Ideal Membership in Polynomial Rings Over the Integers
… of the ring Z p⟨X⟩ of restricted power series with coefficients in the ring Z p of p-adic integers. We also consider the ideal membership problem for ideals of the ring Z p⟨X⟩ itself, and for ideals of its subring Z p⟨X⟩alg consisting of the restricted p-adic …
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Holomorphic Extensions in the Structure R_{an,exp}
… which can be described locally as convergent power series and ask the following: Which real analytic functions definable in R_{an,exp} have a holomorphic extension which is again definable in R_{an,exp}? Finding a holomorphic extension is of course not difficult simply by power series …
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Third-order charged particle beam optics
… from a certain ideal trajectory. One uses power series expansion of the phase-space coordinates to obtain the transfer matrices for a particular optical system.
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