Determination of the Properties of (p, q)‐Sigmoid Polynomials and the Structure of Their Roots
Keyword(s):
Nowadays, many mathematicians have great concern about p q -numbers, which are various applications, and have studied these numbers in many different research areas. We know that p q -numbers are different to q -numbers because of the symmetric property. We find the addition theorem, recurrence formula, and p q -derivative about sigmoid polynomials including p q -numbers. Also, we derive the relevant symmetric relations between p q -sigmoid polynomials and p q -Euler polynomials. Moreover, we observe the structures of appreciative roots and fixed points about p q -sigmoid polynomials. By using the fixed points of p q -sigmoid polynomials and Newton’s algorithm, we show self-similarity and conjectures about p q -sigmoid polynomials.
2012 ◽
Vol 95
(1)
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pp. 157-162
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2000 ◽
Vol 109
(1)
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pp. 31-49
1992 ◽
Vol 66
(5-6)
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pp. 1397-1414
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2003 ◽
Vol 35
(02)
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pp. 395-416
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2017 ◽
Vol 14
(04)
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pp. 1750013
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Keyword(s):
2003 ◽
Vol 35
(2)
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pp. 395-416
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