Примери за използване на Elliptic integrals на Английски и техните преводи на Български
{-}
-
Colloquial
-
Official
-
Medicine
-
Ecclesiastic
-
Ecclesiastic
-
Computer
I refer to elliptic integrals.
Elliptic Integrals of first and second kind.
The third volume was largely devoted to tables of elliptic integrals.
K(m) and E(m)are complete elliptic integrals of the first and second kind, respectively.
Abel's theorem is a vast generalisation of Euler's relation for elliptic integrals.
Talbot wrote papers on elliptic integrals, building on work of Euler, Legendre, Jacobi and Abel.
His work on maxima and minima;the attraction of ellipsoids; elliptic integrals;
He radically transformed the theory of elliptic integrals to the theory of elliptic functions by using their inverse functions….
In 1828 Abel was shown a paper by Jacobi on transformations of elliptic integrals.
Fuchs' study(1876 with Hermite) of elliptic integrals as a function of a parameter marks an important step towards the theory of modular functions(Klein, Dedekind).
In the first volume Legendre introduced basic properties of elliptic integrals and also of beta and gamma functions.
In a short eleven year career Zolotarev produced fundamental work in approximation theory, quadratic forms,algebraic numbers and elliptic integrals.
Where K{\displaystyle\,\! K} and E{\displaystyle\,\! E} are the complete elliptic integrals of the first and second kind respectively.
He published a few papers on elliptic integrals and surface integrals during his career, as well as a number of papers on mathematical education.
He wrote an important text on elliptic functions in 1874 and another important textbook on hyperelliptic integrals four years later.
The paper on the reduction of abelian integrals to simpler elliptic integrals is of less importance but it consisted of a skilled series of manipulations which showed her complete command of Weierstrass 's theory.
Lexell did work in analysis on topics other than differential equations,for example he suggested a classification of elliptic integrals and he worked on the Lagrange series.
Legendre did an impressive amount of work on elliptic functions,including the classification of elliptic integrals, but it took Abel's stroke of genius to study the inverses of Jacobi's functions and solve the problem completely.
He examined multi-valued functions as single valued over a special Riemann surface andsolved general inversion problems which had been solved for elliptic integrals by Abel and Jacobi.
In his writings and problem-solving, Martin dealt mostly with Diophantine analysis,probability, elliptic integrals, logarithms, and properties of numbers and triangles.
Cremona transformations have been used for studying rational surfaces, for the resolution of singularities of plane andspace curves, and for the study of elliptic integrals and Riemann surfaces.
This method of inversion, and its subsequent extension by Weierstrass and Riemann to arbitrary algebraic curves,may be seen as a higher genus generalization of the relation between elliptic integrals and the Jacobi or Weierstrass elliptic functions.
This is an incomplete elliptic integral of the 2nd kind.
This integral is an elliptic integral of the second kind.
And a complete elliptic integral of the second kind.
Where K andΠ are the complete elliptic integral of the first kind and the third kind, respectively.
Its general definition involves the Jacobi elliptic cosine function and the elliptic integral.
Topics Plana worked on, in addition to astronomy,were integrals, elliptic functions, heat, electrostatics and geodesy.
In 1854 Betti showed that the quintic equation could be solved in terms of integrals resulting in elliptic functions.
Galois, after reading Abel and Jacobi's work,worked on the theory of elliptic functions and abelian integrals.