Примери за използване на Continued fractions на Английски и техните преводи на Български
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Congruences and the quadratic reciprocity law; continued fractions;
It also contains continued fractions, quadratic equations, sums of power series and a table of sines.
The thesis studied hyperelliptic andrelated integrals in continued fractions.
Such names as Rogers- Ramanujan identities,Rogers- Ramanujan continued fractions and Rogers transformations are known in the theory of partitions, combinatorics and hypergeometric series.
The book consists of three chapters,the first two of which present the classical theory of continued fractions.
Catalan published extensively on continued fractions and number theory.
In examining periodic solutions of differential equations Bendixson used methods based on continued fractions.
The subject proposed for the Grand Prix of the Paris Academy of 1906 was on the convergence of algebraic continued fractions.
Padé's doctoral supervisor Hermite had used approximants and continued fractions in his work of 1873 on proving the transcendence of e.
He proved results on their general structure andalso clearly set out the connection between Padé approximants and continued fractions.
He is often called"the father of the analytic theory of continued fractions" for his work in this area.
For these eminent services in mathematics, andespecially for your important researches concerning functional equations and analytic continued fractions.
In April 1829 Galois had his first mathematics paper published on continued fractions in the Annales de mathématiques.
Minkowski's original mathematical interests were in pure mathematics andhe spent much of his time investigating quadratic forms and continued fractions.
In addition to the work on continued fractions mentioned above, which in fact ran to three editions the last being a two volume version in 1954/57, he published an important text on irrational numbers in 1921.
Minding also worked on differential equations,algebraic functions, continued fractions and analytic mechanics.
The importance of Khayyam's contribution is that he examined both Euclid's definition of equality of ratios(which was that first proposed by Eudoxus) andthe definition of equality of ratios as proposed by earlier Arab mathematicians such as Al-Mahani which was based on continued fractions.
However he also worked on differential equations, matrices andother topics in algebra, continued fractions, geometry and number theory.
Minkowski was mainly interested in pure mathematics andspent much of his time investigating quadratic forms and continued fractions.
He made substantial contributions to the analyticaltheory of numbers and worked on elliptic functions, continued fractions, and infinite series.
For example he published the ingenious paper Continuous functions defined on spheres in the Annals of Mathematics in 1951, A new symmetry of partitions in 1961, Mappings and symmetries of partitions in 1989, Mean square value of exponential sums related to representation of integers as sum of two squares(jointly with Pavel Bleher)in 1994, and The sixth Fermat number and palindromic continued fractions in 2001.
Christoffel published papers on function theory including conformal mappings, geometry and tensor analysis, Riemann 's o-function, the theory of invariants,orthogonal polynomials and continued fractions, differential equations and potential theory, light, and shock waves.
The second sealed envelope, dated 22 June 1903,contains a paper entitled On a new method for studying the development of certain functions in continued fractions.
At Frankfurt, Hellinger had continued his mathematical work on the spectral theory of Jacobi forms and continued fractions.
Doeblin also contributed to the theory of random chains with complete connection,some of which was used in a paper by him on ergodic properties of continued fractions.
However his contributions led him to prove the existence of a transcendental number in 1844 when he constructed an infinite class of such numbers using continued fractions.
Among the chapter headings are convex bodies in lattices, star bodies, linear forms, minima of homogeneous forms, inhomogeneous forms,definite quadratic forms, continued fractions and algebraic numbers.
Before arriving at Halle, Heine published on partial differential equations and during his first few years teaching at Halle he wrote papers on the theory of heat,summation of series, continued fractions and elliptic functions.