A STUDY ON MULTI-STIRLING NUMBERS OF THE FIRST KIND Article Swipe

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Stirling number Stirling numbers of the second kind Stirling numbers of the first kind Bernoulli number Logarithm Generalization Bell polynomials Mathematics Bernoulli's principle Stirling engine Order (exchange) Bernoulli process Discrete mathematics Combinatorics Mathematical analysis Aerospace engineering Engineering Economics Physics Thermodynamics Finance

Yuankui Ma , Dae San Kim , HYUNSEOK LEE , SEONGHO PARK , TAEKYUN KIM ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.1142/s0218348x22402587 · OA: W4309828084

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.