Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 586 - 598 2020-04-02

Euler sums and non-integerness of harmonic type sums

Haydar GÖRAL [1] , Doğa Can SERTBAŞ [2]


We show that Euler sums of generalized hyperharmonic numbers can be evaluated in terms of Euler sums of generalized harmonic numbers and special values of the Riemann zeta function. Then we focus on the non-integerness of generalized hyperharmonic numbers. We prove that almost all generalized hyperharmonic numbers are not integers and our error term is sharp and the best possible. Finally, we analyze generalized hyperharmonic numbers in terms of topology and relate this to non-integerness.
Harmonic numbers, hyperharmonic numbers, Euler sums
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Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0002-8814-6295
Yazar: Haydar GÖRAL
Kurum: DOKUZ EYLUL UNIVERSITY
Ülke: Turkey


Orcid: 0000-0002-5884-6856
Yazar: Doğa Can SERTBAŞ (Sorumlu Yazar)
Kurum: CUMHURIYET UNIVERSITY
Ülke: Turkey


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms544489, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {586 - 598}, doi = {10.15672/hujms.544489}, title = {Euler sums and non-integerness of harmonic type sums}, key = {cite}, author = {GÖRAL, Haydar and SERTBAŞ, Doğa Can} }
APA GÖRAL, H , SERTBAŞ, D . (2020). Euler sums and non-integerness of harmonic type sums. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 586-598 . DOI: 10.15672/hujms.544489
MLA GÖRAL, H , SERTBAŞ, D . "Euler sums and non-integerness of harmonic type sums". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 586-598 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/544489>
Chicago GÖRAL, H , SERTBAŞ, D . "Euler sums and non-integerness of harmonic type sums". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 586-598
RIS TY - JOUR T1 - Euler sums and non-integerness of harmonic type sums AU - Haydar GÖRAL , Doğa Can SERTBAŞ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.544489 DO - 10.15672/hujms.544489 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 586 EP - 598 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.544489 UR - https://doi.org/10.15672/hujms.544489 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Euler sums and non-integerness of harmonic type sums %A Haydar GÖRAL , Doğa Can SERTBAŞ %T Euler sums and non-integerness of harmonic type sums %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.544489 %U 10.15672/hujms.544489
ISNAD GÖRAL, Haydar , SERTBAŞ, Doğa Can . "Euler sums and non-integerness of harmonic type sums". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 586-598 . https://doi.org/10.15672/hujms.544489
AMA GÖRAL H , SERTBAŞ D . Euler sums and non-integerness of harmonic type sums. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 586-598.
Vancouver GÖRAL H , SERTBAŞ D . Euler sums and non-integerness of harmonic type sums. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 598-586.