On an Iteration Leading to a q-Analogue of the Digamma Function

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Standard

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

Harvard

Berg, C & Petersen, HB 2013, 'On an Iteration Leading to a q-Analogue of the Digamma Function', Journal of Fourier Analysis and Applications, bind 19, nr. 4, s. 762-776. https://doi.org/10.1007/s00041-013-9271-8

APA

Berg, C., & Petersen, H. B. (2013). On an Iteration Leading to a q-Analogue of the Digamma Function. Journal of Fourier Analysis and Applications, 19(4), 762-776. https://doi.org/10.1007/s00041-013-9271-8

Vancouver

Berg C, Petersen HB. On an Iteration Leading to a q-Analogue of the Digamma Function. Journal of Fourier Analysis and Applications. 2013;19(4):762-776. https://doi.org/10.1007/s00041-013-9271-8

Author

Berg, Christian ; Petersen, Helle Bjerg . / On an Iteration Leading to a q-Analogue of the Digamma Function. I: Journal of Fourier Analysis and Applications. 2013 ; Bind 19, Nr. 4. s. 762-776.

Bibtex

@article{450697b882d34ac5a66da94a5c898840,
title = "On an Iteration Leading to a q-Analogue of the Digamma Function",
abstract = "We show that the q-Digamma function ψq for 0 < q < 1 appears in an iteration studied by Berg and Dur{\'a}n. 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.",
author = "Christian Berg and Petersen, {Helle Bjerg}",
year = "2013",
doi = "10.1007/s00041-013-9271-8",
language = "English",
volume = "19",
pages = "762--776",
journal = "Journal of Fourier Analysis and Applications",
issn = "1069-5869",
publisher = "Springer Basel AG",
number = "4",

}

RIS

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