In this paper, we consider the $ q $-type $ k $-Lidstone series. The series follows from expanding certain classes of entire functions in terms of Jackson $ q^{-1} $- derivatives at integers congruent to r modulo k, where $ k $ is a positive integer. We study the main properties of the fundamental polynomials that appear in the series expansion. We include a detailed study for the case $ k = 3 $ with some examples.
Citation: Zeinab S. I. Mansour, Maryam Al-Towailb. A $ q $-Type $ k $-Lidstone series for entire functions[J]. AIMS Mathematics, 2023, 8(6): 13525-13542. doi: 10.3934/math.2023686
In this paper, we consider the $ q $-type $ k $-Lidstone series. The series follows from expanding certain classes of entire functions in terms of Jackson $ q^{-1} $- derivatives at integers congruent to r modulo k, where $ k $ is a positive integer. We study the main properties of the fundamental polynomials that appear in the series expansion. We include a detailed study for the case $ k = 3 $ with some examples.
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Zeinab S. I. Mansour, Maryam Al-Towailb. A $ q $-Type $ k $-Lidstone series for entire functions[J]. AIMS Mathematics, 2023, 8(6): 13525-13542. doi: 10.3934/math.2023686
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