Abstract
We show that the q-Digamma function ψq for 0 < q < 1 appears in an
iteration studied by Berg and Durán. This is connected with the determination of the probability measure νq on the unit interval with moments 1/n+1 k=1(1 − q)/(1 −
qk), which are q-analogues of the reciprocals of the harmonic numbers. The Mellin transform of the measure νq can be expressed in terms of the q-Digamma function.
It is shown that νq has a continuous density on ]0, 1], which is piecewise C∞ with kinks at the powers of q. Furthermore, (1 − q)e−xνq (e−x ) is a standard p-function from the theory of regenerative phenomen.
iteration studied by Berg and Durán. This is connected with the determination of the probability measure νq on the unit interval with moments 1/n+1 k=1(1 − q)/(1 −
qk), which are q-analogues of the reciprocals of the harmonic numbers. The Mellin transform of the measure νq can be expressed in terms of the q-Digamma function.
It is shown that νq has a continuous density on ]0, 1], which is piecewise C∞ with kinks at the powers of q. Furthermore, (1 − q)e−xνq (e−x ) is a standard p-function from the theory of regenerative phenomen.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Journal of Fourier Analysis and Applications |
| Vol/bind | 19 |
| Udgave nummer | 4 |
| Sider (fra-til) | 762-776 |
| ISSN | 1069-5869 |
| DOI | |
| Status | Udgivet - aug. 2013 |