Open AccessREPRESENTATION OF SOME SPECIAL FUNCTIONS ON TRANSCENDENCE BASIS
Author(s) -
Chien Van Bui
Publication year - 2020
Publication title -
tạp chí khoa học đại học huế: khoa học tự nhiên/tạp chí khoa học đại học huế: khoa học tự nhiên (online)
Language(s) - English
Resource type - Journals
eISSN - 2615-9678
pISSN - 1859-1388
DOI - 10.26459/hueuni-jns.v129i2a.5636
Subject(s) - transcendence (philosophy) , mathematics , algebra over a field , pure mathematics , polylogarithm , representation (politics) , commutative property , polynomial , special functions , basis (linear algebra) , harmonic , series (stratigraphy) , mathematical analysis , riemann zeta function , epistemology , geometry , paleontology , philosophy , physics , prime zeta function , quantum mechanics , arithmetic zeta function , politics , political science , law , biology
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.