On an Iteration Leading to a q-Analogue of the Digamma Function
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On an Iteration Leading to a q-Analogue of the Digamma Function. / Berg, Christian; Petersen, Helle Bjerg .
I: Journal of Fourier Analysis and Applications, Bind 19, Nr. 4, 2013, s. 762-776.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - On an Iteration Leading to a q-Analogue of the Digamma Function
AU - Berg, Christian
AU - Petersen, Helle Bjerg
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
U2 - 10.1007/s00041-013-9271-8
DO - 10.1007/s00041-013-9271-8
M3 - Journal article
VL - 19
SP - 762
EP - 776
JO - Journal of Fourier Analysis and Applications
JF - Journal of Fourier Analysis and Applications
SN - 1069-5869
IS - 4
ER -
ID: 49738302