Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling
Abstract
:1. Introduction
2. Preliminaries
3. The Frobenius–Euler–Genocchi Polynomials
4. Some Applications of Frobenius–Euler–Genocchi Polynomials of Order
5. Further Remarks
6. Computational Values and Graphical Representations of Frobenius–Euler–Genocchi Polynomials
7. Computational Values and Graphical Representations of Changhee–Frobenius–Euler–Genocchi Polynomials
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Degree | |
---|---|
3 | −0.50000 |
4 | −0.50000 − 0.86603i, −0.50000 + 0.86603 i |
5 | −1.0800, −0.2100 − 1.5819 i, −0.2100 + 1.5819 i |
6 | −1.1991 − 0.7701 i, −1.1991 + 0.7701 i, |
0.1991 − 2.2101 i, 0.1991 + 2.2101 i | |
7 | −1.6268, −1.1130 − 1.4787i, −1.1130 + 1.4787 i, |
0.6764 − 2.7763 i, 0.6764 + 2.7763 i | |
8 | −1.7906 − 0.7321 i, −1.7906 + 0.7321i, −0.9087 − 2.1385 i, |
−0.9087 + 2.1385 i, 1.1993 − 3.2957i, 1.1993 + 3.2957 i | |
9 | −2.1611, −1.7990 − 1.4290 i, −1.7990 + 1.4290 i, −0.6261 − 2.7580 i, |
−0.6261 + 2.7580 i, 1.7556 − 3.7778 i, 1.7556 + 3.7778 i | |
10 | −2.3477 − 0.7111 i, −2.3477 + 0.7111 i, −1.7030 − 2.0940 i, |
−1.7030 + 2.0940 i, −0.2870 − 3.3436 i, −0.2870 + 3.3436 i, | |
2.3378 − 4.2296 i, 2.3378 + 4.2296 i | |
11 | −2.6889, −2.4100 − 1.3992 i, −2.4100 + 1.3992 i, |
−1.5315 − 2.7306 i, −1.5315 + 2.7306 i, 0.0952 − 3.8998 i, | |
0.0952 + 3.8998 i, 2.9407 − 4.6560 i, 2.9407 + 4.6560 i |
Degree | |
---|---|
3 | 1.2500 |
4 | 0.97272, 2.5273 |
5 | 0.83715, 2.2045, 3.7084 |
6 | 0.75834, 2.0289, 3.3703, 4.8425 |
7 | 0.70700, 1.9225, 3.1696, 4.5035, 5.9475 |
8 | 0.67047, 1.8533, 3.0413, 4.2873, 5.6152, 7.0324 |
9 | 0.64266, 1.8052, 2.9562, 4.1418, 5.3905, 6.7113, 8.1024 |
10 | 0.62043, 1.7695, 2.8973, 4.0421, 5.2320, 6.4829, 7.7949, 9.1609 |
11 | 0.60202, 1.7414, 2.8545, 3.9723, 5.1194, 6.3151, 7.5666, 8.8684, 10.210 |
12 | 0.58638, 1.7185, 2.8218, 3.9220, 5.0389, 6.1915, 7.3925, 8.6427, 9.9333, 11.252 |
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Alam, N.; Khan, W.A.; Kızılateş, C.; Obeidat, S.; Ryoo, C.S.; Diab, N.S. Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling. Symmetry 2023, 15, 1358. https://doi.org/10.3390/sym15071358
Alam N, Khan WA, Kızılateş C, Obeidat S, Ryoo CS, Diab NS. Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling. Symmetry. 2023; 15(7):1358. https://doi.org/10.3390/sym15071358
Chicago/Turabian StyleAlam, Noor, Waseem Ahmad Khan, Can Kızılateş, Sofian Obeidat, Cheon Seoung Ryoo, and Nabawia Shaban Diab. 2023. "Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling" Symmetry 15, no. 7: 1358. https://doi.org/10.3390/sym15071358
APA StyleAlam, N., Khan, W. A., Kızılateş, C., Obeidat, S., Ryoo, C. S., & Diab, N. S. (2023). Some Explicit Properties of Frobenius–Euler–Genocchi Polynomials with Applications in Computer Modeling. Symmetry, 15(7), 1358. https://doi.org/10.3390/sym15071358