A q-analogue for Euler’s ζ(6) =π6/945

Description

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

Period	23 Jul 2019
Event title	15th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA)
Event type	Conference
Location	AustriaShow on map