NONLINEAR DIFFERENTIAL EQUATIONS AND LEGENDRE POLYNOMIALS

키워드

참고문헌 (34)

1. S. Abbasbandy, "Applica-tion of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation", Appl. Math. Comput, 266, pp.31~40 (2015)
2. M. Abramowitz, "Handbook of mathematical functions with for-mulas, graphs, and mathematical tables" (1964), For sale by the Superintendent of Documents, U.S. Government Printing Office
3. G. E. Albert, "Asymtotic forms for a general class of hypergeometric func-tions with aapplication to the generalized Legendre functions", Duke. Math. J, 5(2), pp.281~292 (1939)
4. G. B. Arfken, "Mathematical methods for physicists", pp.2001, Harcourt
5. V. M. Babich, "To the problem on the asymptotics with respect to the indices of the associated Legendre function", Russ. J. Math. Phys, 9(1), pp.6~13 (2002)
6. W. N. Bailey, "On the Product of two Legendre Polynomials with Different Ar-guments", Proc. London Math. Soc, S2-41(3), pp.215~
7. 2006, , ~
8. D. Beckwith, "Notes: Legendre Polynomials and Polygon Dissections?", Amer. Math. Monthly, 105(3), pp.256~257 (1998)
9. S. L. Belousov, "Tables of normalized associated Legendre polynomials" (1962), Pergamon Press
10. W. C. Brenke, "On the summability and generalized sum of a series of Legendre polynomials", Bull. Amer. Math. Soc, 39(10), pp.821~824 (1933)
11. L. Carlitz, "Some arithmetic properties of the Legendre polynomials", Acta Arith, 4, pp.99~107 (1958)
12. L. Carlitz, "Some congruence properties of the Legendre polynomials", Math. Mag, 34, pp.387~390 (1960)
13. L. Carlitz, "Some integrals containing products of Legendre polynomials", Arch. Math, 12, pp.334~340 (1961)
14. C.-Y. Chen, "The origin and math-ematical characteristics of the super-universal associated-Legendre polynomials", Commun. Theor. Phys. (Beijing), 62(3), pp.331~337 (2014)
15. Y. M. Chen, "Based on fractional-order Le-gendre functions solving a class of fractional-order differential equations", Math. Numer. Sin, 37(1), pp.21~33 (2015)
16. S. Choi, "Relation between primes and nontrivial zeros in the Riemann hypothesis, Legendre polynomials, modified zeta func-tion and Schrodinger equation", J. Math. Phys, 53(12), pp.122108~ (2012)
17. R. Courant, "Methods of mathematical physics. Vol. I" (1953), Inter-science Publishers, Inc.
18. G. Dattoli, "The Laguerre and Legendre poly-nomials from an operational point of view", Appl. Math. Comput, 124(1), pp.117~127 (2001)
19. M. Hazewinkel, "Legendre polynomials, Encyclopedia of Mathematics" (2001), Springer
20. I. R. Horng, "Design of optimal observers with specified eigenval-ues via shifted Legendre polynomials", J. Optim. Theory Appl, 51(1), pp.179~188 (1986)
21. J. D. Jackson, "Classical electrodynamics" (1975), John Wiley & Sons, Inc.
22. H. Khalil, "New operational matrix of shifted Legendre polynomials and fractional differential equations with variable coefficients", Punjab Univ. J. Math. (Lahore), 47(1), pp.81~103 (2015)
23. 김대산, "SOME IDENTITIES FOR BERNOULLI NUMBERS OF THE SECOND KIND ARISING FROM A NON-LINEAR DIFFERENTIAL EQUATION", 대한수학회보, 52(6), pp.2001~2010 (2015), 대한수학회
24. D. S. Kim, "Some identities on Bernoulli and Euler poly-nomials arising from orthogonality of Legendre polynomials", J. Inequal. Appl, 2012(227), pp.8~ (2012)
25. T. Kim, "Identities involving Laguerre polynomials derived from umbral calculus", Russ. J. Math. Phys, 21(1), pp.36~45 (2014)
26. T. Kim, "Degenerate Euler zeta function", Russ. J. Math. Phys, 22(4), pp.469~472 (2015)
27. T. H. Koornwinder, "Orthogonal polynomials, NIST handbook of mathematical functions", U.S. Dept. Commerce, 435~484 (2010)
28. D. V. Kurdomonov, "An estimate for the rate of convergence of Fourier-Legendre series of functions of bounded variation", Izv. Vyssh. Uchebn. Zaved. Mat, (7), pp.34~45 (2006)
29. J. Kwon, "A note on (h, q)-Boole polynomials", Adv. Difference Equ, 2015(198), pp.11~ (2015)
30. P. Mokhtary, "The Muntz-Legendre Tau method for fractional differential equations", Appl. Math. Model, 40(2), pp.671~684 (2016)
31. E. A. Refaat, "Legendre polynomials and functions" (2009), CreateSpace
32. D. Rostamy, "Discontinuous Petrov-Galerkin and Bernstein-Legendre polynomials method for solving fractional damped heat- and wave-like equations", J. Comput. Theor. Transp, 44(1), pp.1~23 (2015)
33. M. H. Stone, "Developments in Legendre polynomials", Ann. of Math. (2), 27(4), pp.315~329 (1926)
34. D. G. Zill, "Advanced Engineering Mathematics" (2009), Jones&Bartlett Publishers

관련 논문AI추천