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Noncommutative Continued Fractions
SIAM Journal on Mathematical Analysis, 1971A number of theorems are proved concerning the convergence of continued fractions whose entries are linear operators on a Banach space. These theorems are analogues of some of the well-known results for ordinary continued fractions.
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Generalized continued fractions
Applied Mathematics and Computation, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Ramanujan's Continued Fraction
Mathematical Proceedings of the Cambridge Philosophical Society, 1935The best of the theorems on continued fractions, to be found in Ramanujan's manuscript note-book may be stated as follows:where there are eight gamma-functions in each product and the ambiguous signs are so chosen that the argument of each gamma-function contains one of the specified numbers of minus signs.
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Continued Fractions Continued, Applications
1989We are now ready to explain the Brillhart-Morrison Continued Fraction Algorithm (commonly known as CFRAC) for factoring large numbers. The original idea is actually due to D. H. Lehmer and R. E. Powers in 1931 and it draws much of its inspiration from Legendre who used the continued fraction expansion in a procedure that restricted the congruence ...
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The Mathematics Teacher, 1962
An opportunity for the teacher to set before his students situations which will stimulate creative ...
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An opportunity for the teacher to set before his students situations which will stimulate creative ...
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1991
Abstract The mathematical techniques developed and deployed so far in the historical reconstructions of this book have not been arithmetised; that is, they have not been expressed in terms of some model, explicit or implicit, of the real numbers and its arithmetic. This chapter will be different.
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Abstract The mathematical techniques developed and deployed so far in the historical reconstructions of this book have not been arithmetised; that is, they have not been expressed in terms of some model, explicit or implicit, of the real numbers and its arithmetic. This chapter will be different.
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Abstract A thorough exposition of finite simple continued fractions is given. All rational numbers have such representations. Convergents to a simple continued fraction is studied and a handy algorithm is developed which helps to readily compute them. The uniqueness of a continued fraction representation is covered.
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2017
This thesis is not available on this repository until the author agrees to make it public. If you are the author of this thesis and would like to make your work openly available, please contact us: thesis@repository.cam.ac.uk.
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This thesis is not available on this repository until the author agrees to make it public. If you are the author of this thesis and would like to make your work openly available, please contact us: thesis@repository.cam.ac.uk.
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Plant rhizodeposition: A key factor for soil organic matter formation in stable fractions
Science Advances, 2021Sebastián Horacio Villarino +2 more
exaly