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A Study On Multi-Stirling Numbers Of The First Kind

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yuankui Ma & Dae San Kim & Hyunseok Lee & Seongho Park & Taekyun Kim, 2022. "A Study On Multi-Stirling Numbers Of The First Kind," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-7, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402587
    DOI: 10.1142/S0218348X22402587
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