On parametric types of Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials via Golden calculus

Can Kızılateş; Halit Öztürk; Can Kızılateş; Halit Öztürk

doi:10.3934/math.2023423

AIMS Mathematics

2023, Volume 8, Issue 4: 8386-8402. doi: 10.3934/math.2023423

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Research article

On parametric types of Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials via Golden calculus

Can Kızılateş ^,,
Halit Öztürk

Zonguldak Bülent Ecevit University, Faculty of Sciences, Department of Mathematics, TR-67100 Zonguldak, Turkey

Received: 06 December 2022 Revised: 16 January 2023 Accepted: 19 January 2023 Published: 03 February 2023
MSC : 11B68, 11B83, 05A15, 05A19

This paper aims to give generating functions for the new family of polynomials, which are called parametric types of the Apostol Bernoulli-Fibonacci, the Apostol Euler-Fibonacci, and the Apostol Genocchi-Fibonacci polynomials by using Golden calculus. Numerous properties of these polynomials with their generating functions are investigated. These generating functions give us a generalization of some well-known generating functions for special polynomials such as Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials. Using the Golden differential operator technique, the functional equation method for generating function, we present some properties of these newly established polynomials.
- Appell polynomials,
- Golden calculus,
- generating functions,
- determinants
Citation: Can Kızılateş, Halit Öztürk. On parametric types of Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials via Golden calculus[J]. AIMS Mathematics, 2023, 8(4): 8386-8402. doi: 10.3934/math.2023423

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Abstract

This paper aims to give generating functions for the new family of polynomials, which are called parametric types of the Apostol Bernoulli-Fibonacci, the Apostol Euler-Fibonacci, and the Apostol Genocchi-Fibonacci polynomials by using Golden calculus. Numerous properties of these polynomials with their generating functions are investigated. These generating functions give us a generalization of some well-known generating functions for special polynomials such as Apostol Bernoulli-Fibonacci, Apostol Euler-Fibonacci, and Apostol Genocchi-Fibonacci polynomials. Using the Golden differential operator technique, the functional equation method for generating function, we present some properties of these newly established polynomials.

References

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