Polylogarithmes
Polylogarithmic functional equations: A new category of results developed with the help of computer algebra (MACSYMA).
Polylogarithms in the field of omega (a root of given cubic): Functional equations and ladders.
Polynomial approximation to integral transforms
Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus
Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs...
Polynomial functions on the classical projective spaces
The polynomial functions on a projective space over a field = ℝ, ℂ or ℍ come from the corresponding sphere via the Hopf fibration. The main theorem states that every polynomial function ϕ(x) of degree d is a linear combination of “elementary” functions .
Polynomials associated with dihedral groups.
Positivity of Cotes Numbers at More Jacobi Abscissas.
Positivity of the Cotes Numbers for some Jacobi Abscissas.
Powers and Logarithms
There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers...
Poznámka k Favardově větě
Poznámka o funkci
Poznámka o sférické trigonometrii
Poznámka o výpočtu čísla:
Poznánka k substituci Landenově
Priority, parallel discovery, and pre-eminence Napier, Bürgi and the early history of the logarithm relation
There has never been any doubt as to the importance of the logarithm, a mathematical relation whose usefulness has persisted in different aspects to the present day. Within years of their introduction, logarithms became indispensable for mathematicians, astronomers, navigators, and geographers alike. The question of their origins, however, is more contentious. At least two scholars, the Scottish nobleman John Napier and the Swiss craftsman Jost Bürgi, simultaneously and independently produced proposals...
Příspěvek k elementarné theorii elliptických integrálů. [I.]
Příspěvek k elementarné theorii elliptických integrálů. [II.]
Přispěvek k theorii transformace elliptických integrálů
Příspěvek ku transformaci jedenáctého řádu funkcí elliptických