A q-analogue for Euler’s ζ(6) =π6/945

Beschreibung

Recently, Z.-W. Sun obtained q-analogues of Euler’s formula for ζ(2) and ζ(4). Sun’s formula were based on identities satisfied by triangular numbers and properties of Euler’s q-Gamma function. Inthis talk, we discuss a q-analogue of ζ(6) =π6/945. Indeed, we have been able to obtainq-analogues of Euler’s formula for ζ(2k), k= 4,5,...(the general case). However, it is to be noted here that the case k= 3 or theq-analogue of ζ(6) is striking as it leads to very interesting connections. Also, the q-analogue of ζ(6) is the first non-trivial case where we see the occurence of a certain “extra” term which goes to zero as q→1 from inside the unit disk. We will also shed some light on this extra term

Zeitraum	23 Juli 2019
Ereignistitel	15th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA)
Veranstaltungstyp	Konferenz
Ort	Hagenberg, ÖsterreichAuf Karte anzeigen