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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제58권 제5호
- 발행연도
- 2021.9
- 수록면
- 1,079 - 1,095 (17page)
- DOI
- 10.4134/BKMS.b200359
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초록· 키워드
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In this paper, we give new congruences with the generalized Catalan numbers and harmonic numbers modulo $p^{2}.$ One of our results is as follows: for prime number $p>3,$ \begin{align*} &\sum\limits_{k=(p+1)/2}^{p-1}k^{2}B_{p,k}B_{p,k-(p-1)/2}H_{k}\equiv \left( -1\right) ^{(p-1)/2}\left( -\frac{521}{36}p-\frac{1}{p}-\frac{41}{12}\right. \\ &\text{ \ \ \ \ \ \ \ }\left. +pH_{3(p-1)/2}^{2}-10pq_{p}^{2}(2)+4\left( \frac{10}{3}p+1\right) q_{p}(2)\right) \pmod{p^{2}}, \end{align*} where $q_{p}(2)$ is Fermat quotient.
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참고문헌 (19)
참고문헌 신청
N. H. Abel / 1826 / Untersuchungen ¨uber die Reihe 1+ m 1x+m(m−1)1.2x 2+m(m−1)(m−2)1.2.3x 3+· · · / Journal für die reine und angewandte Mathematik (Crelles Journal) 1:311~339
Horst Alzer / 2006 / Series representations for some mathematical constants / Journal of Mathematical Analysis and Applications 320(1):145~162
Xiaojing Chen / 2009 / Moments on Catalan numbers / Journal of Mathematical Analysis and Applications 349(2):311~316
Junesang Choi / 2011 / Some summation formulas involving harmonic numbers and generalized harmonic numbers / Mathematical and Computer Modelling 54(9-10):2220~2234
Emeric Deutsch / 2001 / A survey of the Fine numbers / Discrete Mathematics 241(1-3):241~265
Horst Alzer / 2006 / Series representations for some mathematical constants / Journal of Mathematical Analysis and Applications 320(1):145~162
Xiaojing Chen / 2009 / Moments on Catalan numbers / Journal of Mathematical Analysis and Applications 349(2):311~316
Junesang Choi / 2011 / Some summation formulas involving harmonic numbers and generalized harmonic numbers / Mathematical and Computer Modelling 54(9-10):2220~2234
Emeric Deutsch / 2001 / A survey of the Fine numbers / Discrete Mathematics 241(1-3):241~265
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