Representation of some special functions on transcendence basis

The special functions such as multiple harmonic sums, polyzetas or multiple polylogarithm functions are compatible with quasi-shuffle algebras. By using transcendence bases of the quasi-shuffle algebras studied in the paper [4], we will express non-commutative generating series of these special functions and then identify on the local coordinates to reduce their polynomial relations or asymptotic expansions indexed by these bases.

REPRESENTATION OF SOME SPECIAL FUNCTIONS ON TRANSCENDENCE BASIS

The special functions such as multiple harmonic sums, polyzetas or multiple polylogarithm functions are compatible with quasi-shuffle algebras. By using transcendence bases of the quasi-shuffle algebras studied in the paper [4], we will express non-commutative generating series of these special functions and then identify on the local coordinates to reduce their polynomial relations or asymptotic expansions indexed by these bases.

E.HUSSERL’S PHENOMENOLOGY AS AN EXISTENTIAL TRANSCENDENCE BASIS

<p>This article is an attempt to overcome the epistemological interpretation of the practical importance of the «matter of feelings» in favor of the introduction of the existential Absolutes as a phenomenological «matter», constructed by us in a “loaded” natural setting. The authors rely on the basic provisions of phenomenological philosophy, detailed in such Husserl’s works as the “Logical investigations”, “Ideas for a pure phenomenology”, “Phenomenology of the Internal Consciousness of Time.” The authors propose a more expansive interpretation of such concepts as «intention», «operation noesis», «internal consciousness of time.» As a unifying moment of the psyche the authors used Carl Jung’s concept of «Ego», in which they insert the corresponding phenomenological implications. We are in the chains of our own mentality, for it is only through it that we can obey. A poor appearance in the world requires from «Ego» immediate opportunities to live in piled formation natural settings, recreating thus the fundamental original experiences of the subjects. Meanwhile, following the perfect schemes of everyday life, we recreate the existential transparent myth as the focus of opposing Absolutes. Absolutes derive from universal, precluding any differentiation. «Ego», absorbed by «urgent matters», seeks to satisfy nothing but its own needs, devoid at times of choice, despite the fact that the choice, like everything else, is only in our minds.<strong></strong></p>