A STUDY ON MULTI-STIRLING NUMBERS OF THE FIRST KIND

Yuankui Ma, Dae San Kim, Hyunseok Lee, Seongho Park and Taekyun Kim
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Yuankui Ma: School of Science, Xi’an Technological University, Xi’an, Shaanxi 710021, P. R. China
Dae San Kim: ��Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
Hyunseok Lee: ��Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Seongho Park: ��Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Taekyun Kim: School of Science, Xi’an Technological University, Xi’an, Shaanxi 710021, P. R. China‡Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-7

Abstract: In this paper, we define the multi-Stirling numbers of the first kind by means of the multiple logarithm and as a generalization of the Stirling numbers of the first kind. Then we introduce two additional special numbers by using the multiple logarithm, namely the modified multi-Bernoulli numbers as a generalization of the higher-order Bernoulli numbers and the multi-Lah numbers of type 2 as a generalization of the Lah numbers. For both of these special numbers, we derive explicit expressions for them which involve the multi-Stirling numbers of the first kind.

Keywords: Multi-Stirling Numbers of the First Kind; Modified Multi-Bernoulli Numbers; Multi-Lah Numbers of Type 2 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402587

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