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布巴克爾多項式

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布巴克爾多項式

[編輯]

在數學中,布巴克爾 多項式 [1]有兩種常見定義。第一種是 :

有時也會使用另一種定義,可以通過遞歸的方式進行定義。首先,規定前三 個布巴克爾多項式為:

然後運用下面的遞推關係得到更高階的多項式。

布巴克爾 多項式也可以用母函數表示 :

產生了許多整數序列在On-Line Encyclopedia of Integer Sequences (OEIS)[2] e PlanetMath頁面存檔備份,存於網際網路檔案館).

生成解

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布巴克爾 多項式的通解為 :


微分操作代表

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布巴克爾 多項式亦可記為 :

用途

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布巴克爾 多項式的 用途:


參考文獻

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  1. ^ Oyodum, OD; Awojoyogbe, OB; Dada, MK.; Magnuson, JN, On the earliest definition of the 布巴克尔 polynomials, Eur. Phys. J. Appl. Phys.: 21201–21202, [2011-08-04], (原始內容存檔於2011-10-05) 
  2. ^ Sequences A135929 and A135936 by Neil J. A. Sloane, A137276 , Roger L. Bagula , Gary Adamson,A138476, A. Bannour, A137289, A136256, A136255 , R. L. Bagula 在 On-Line Encyclopedia of Integer Sequences
  3. ^ Book:Cryogenics: Theory, Processes and Applications, Chapter 8: Cryogenics Vessels Thermal Profilng Using the 布巴克尔 Polynomials Expansion Scheme Investigation , Editor: Allyson E.Hayes, [2011-08-04], (原始內容存檔於2012-10-11) 
  4. ^ B. Dubey, T.G. Zhao, M. Jonsson, H. Rahmanov, A solution to the accelerated-predator-satiety Lotka–Volterra predator–prey problem using 布巴克尔 polynomial expansion scheme, Journal of Theoretical Biology (Elsevier), {{doi:10.1016/j.jtbi.2010.12.002}} 
  5. ^ A. Milgeam, The stability of the 布巴克尔 polynomials expansion scheme (BPES)-based solution to Lotka–Volterra problem, Journal of Theoretical Biology (Elsevier), {{doi:10.1016/j.jtbi.2010.01.026}} 
  6. ^ H. Koçak, A. Yıldırım, D.H. Zhang, S.T. Mohyud-Din, The Comparative 布巴克尔 Polynomials Expansion Scheme (BPES) and Homotopy Perturbation Method (HPM) for solving a standard nonlinear second-order boundary value problem, Mathematical and Computer Modelling(Elsevier), {{doi:10.1016/j.mcm.2011.02.031 }} 
  7. ^ A. Yildirim, The 布巴克尔 polynomials expansion scheme for solving nonlinear science problems, (PDF), The 7th International Conference on Differential Equations and Dynamic Systems, University of South Florida, Tampa, Fmorida USA, 15-18 December 2010 <Page 40 >, (原始內容 (PDF)存檔於2011年7月22日) 
  8. ^ Paul Barry, Aoife Hennessy, Meixner-Type Results for Riordan Arrays and Associated Integer Sequences, Chapter 6: The 布巴克尔 polynomials (PDF), Journal of Integer Sequences (JIS), [2011-08-04], (原始內容存檔 (PDF)於2018-04-28) 
  9. ^ H. Koçak, Z. Dahong, A. Yildirim, A range-free method to determine antoine vapor-pressure heat transfer-related equation coefficients using the 布巴克尔 polynomials expansion scheme, Russian Journal of Physical Chemistry A, Focus on Chemistry (Springer) [永久失效連結]
  10. ^ H. Koçak, Z. Dahong, A. Yildirim, Analytical expression to temperature-dependent Kirkwood-Fröhlich dipole orientation parameter using the 布巴克尔 Polynomials Expansion Scheme (BPES), Indian Journal of Physics(Springer) [永久失效連結]
  11. ^ A. Belhadj, O. F. Onyango and N. Rozibaeva, 布巴克尔 Polynomials Expansion Scheme-Related Heat Transfer Investigation Inside Keyhole Model (PDF), Jornal of Thermophysics and Heat Transfer (American Institute of Aeronautics and Astronautics) AIAA) [永久失效連結]
  12. ^ D. H. Zhang, Study of a non-linear mechanical system using 布巴克尔 polynomials expansion scheme BPES, International Journal of Non-Linear Mechanics(Elsevier) 
  13. ^ Emna Gargouri-Ellouze, Noreen Sher Akbar, Sohail Nadeem, Modelling Nonlinear Bivariate Dependence Using the 布巴克尔 Polynomials Copula The 布巴克尔 polynomials (PDF), Studies in Nonlinear Sciences (SNS), [2011-08-04], (原始內容存檔 (PDF)於2020-09-22) 
  14. ^ W. X. Yue, H. Koçak, D. H. Zhang , A. Yıldırım, A second attempt to establish an analytical expression to steam-water dipole orientation parameter using the 布巴克尔 polynomials expansion scheme, Journal of Structural Chemistry (Springer) [永久失效連結]
  15. ^ D. H. Zhang, L. Naing, The 布巴克尔 polynomials expansion scheme BPES for solving a standard boundary value problem (PDF), Applied Sciences,(Balkan Society of Geometers, Geometry Balkan Press), [2011-08-04], (原始內容存檔 (PDF)於2020-09-28) 
  16. ^ A. Belhadj, J. Bessrour, M. Bouhafs and L. Barrallier, Experimental and theoretical cooling velocity profile inside laser welded metals using keyhole approximation and 布巴克尔 polynomials expansion, Journal of Thermal Analysis and Calorimetry(Akadémiai Kiadó, Springer Science & Kluwer Academic Publishers B.V.), {{doi:10.1007/s10973-009-0094-4 }} [永久失效連結]
  17. ^ S. Amir Hossein A. E. Tabatabaei, T. Gang Z., O. Bamidele A. and Folorunsho O. Moses, Cut-off cooling velocity profiling inside a keyhole model using the 布巴克尔 polynomials expansion scheme, Heat and Mass Transfer(Springer Berlin / Heidelberg), Volume 45, Number 10 / août 2009, pages:1247-1251 {{doi:10.1007/s00231-009-0493-x}} [永久失效連結]
  18. ^ S. Fridjine and M. Amlouk, A NEW PARAMETER-ABACUS FOR OTIMIZING PV-T HYBRID SOLAR DEVICES FUNCTIONAL MATERIALS USING 布巴克尔 POLYNOMIALS EXPANSION SCHEME, Modern Physics Letters B ([ISSN: 0217-9849, by WS: World Scientific Publishing Co Pte Ltd] ) 
  19. ^ T. G. Zhao, Y. X. Wang and K. B. Ben Mahmoud, Limit and uniqueness of the 布巴克尔-Zhao polynomials single imaginary root sequence, International Journal of Mathematics and Computation, ISSN 0974-5718, (原始內容存檔於2011-08-13) 
  20. ^ Luzon, A.; Moron, M., RECURRENCE RELATIONS FOR POLYNOMIAL SEQUENCES VIA RIORDAN MATRICES, Pages 24-25: 布巴克尔 POLYNOMIALS associated Riordan matrix (PDF) 
  21. ^ B. Tirimula Rao, P. Srinivsu, C. Anantha Rao, K. Satya Vivek Vardhan, Jami Vidyadhari ,Page 8 : 布巴克爾 polynomials
  22. ^ Kiliç Bülent, Erdal Bas, Page 7, Citation 27: 布巴克尔 polynomials (PDF). [2011-08-04]. (原始內容存檔 (PDF)於2018-04-20). 

外部連結

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a New Parameter:. AN Abacus for Optimizing Pv-T Hybrid Solar Device Functional Materials Using the 布巴克尔 多項式 Expansion Scheme, [2011-08-04], (原始內容存檔於2017-05-24)  and [1]
De Khawarizmi à Euler, La Presse Magazine, January 9, 2008 [2011-08-04], (原始內容存檔於2012-03-29)  (法文), vedi anche tunisie7arts.com
Le polynôme de 布巴克尔 (PDF), La Presse Magazine, April 22, 2007, (1019): 6 [永久失效連結] (法文)
A new polynomial sequence... The 布巴克尔 Polynomials, Numerical Methods for Partial Differential Equations NMPDE [永久失效連結]
Solution to Heat Equation Using 布巴克尔 Polynomials (PDF), J. of Thermophysics and Heat Transfer [永久失效連結]
布巴克尔 多項式 Weak Solutions to a Robin Boundary Conditioned Dynamic-State Heat Transfer Problem, International Journal of Heat Transfer 
  • WS World Scientific Publishing Co Pte Ltd
AMLOUK–布巴克尔 EXPANSIVITY..USING 布巴克尔 多項式, Functional Materials Letter 
  • Pubblicazioni accademiche
A new polynomial sequence ...The 布巴克尔 Polynomials, International Journal of Applied Mathematics, [2011-08-04], (原始內容存檔於2021-04-05) 
  • 其他文件:
., Journal of Crystal Growth 
., Current appied physics 
Sciendedirect.com頁面存檔備份,存於網際網路檔案館): . , . , . ,., Journal of Alloys and Compounds ,. . ,. , . , ., Material Letters , ., Thermochimica Acta 
  • ENEA Ente Nazionale per le Energie Alternative
An attempt... using 布巴克尔 多項式, International Journal of Heat and Technology, [2011-08-04], (原始內容存檔於2015-06-29) 
Numerical Distribution of Temperature During Welding Using 布巴克尔 Polynomials, Numerical Heat Transfer, Part A, Applications 
Establishment of an Ordinary Generating Function and a Christoffel-Darboux Type First-Order Differential Equation for the Heat Equation Related 布巴克尔-Turki Polynomials (PDF), Journal of Differential Equations and C.P. 
Some new properties of the applied-physics related 布巴克尔 polynomials (PDF), [2011-08-04], (原始內容存檔 (PDF)於2012-02-12)