Bibliography for Legendre polynomials

unabridged

 

  1. On the interval Legendre polynomials
    Patricio, F.; Ferreira, J.A.; Oliveira, F.
    Journal of Computational and Applied Mathematics, v 154, n 1, May 1, 2003, p 215-227, Compendex.  
  2. Polynomial solutions of the classical equations of Hermite, Legendre, and Chebyshev
    Levine L.E.; Maleh R.
    International Journal of Mathematical Education in Science and Technology, 2003, vol. 34, no. 1, pp. 95-103(9), Ingenta.
  3. One-parameter sea water light scattering phase function in the form of legendre polynomial series
    Haltrin, Vladimir I.  
    Oceans Conference Record (IEEE), v 5, 2003, p P2842-P2844, Compendex.  
  4. Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces.  
    Kim, D. H.; Kim, S. H.; Kwon, K. H.; Li, Xin
    Constr. Approx.  18  (2002),  no. 4, 551--568, MathSciNet.  
  5. Acoustic wave propagation in continuous functionally graded plates: An extension of the Legendre polynomial approach
    Lefebvre, J.E.; Zhang, V.; Gazalet, J.; Gryba, T.; Sadaune, V.
    IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, v 48, n 5, September, 2001, p 1332-1340, Compendex.  
  6. Little q-Legendre Polynomials and Irrationality of Certain Lambert Series
    Author: Van Assche W.
    The Ramanujan Journal, September 2001, vol. 5, no. 3, pp. 295-310(16), Ingenta.
  7. Application of Chebyshev and Legendre polynomials on discrete point set to function interpolation and solving Fredholm integral equations
    Streltsov, I.P.  
    Computer Physics Communications, v 126, n 1, Apr, 2000, p 178-181, Compendex.  
  8. Approximation of the partial sums of Legendre-Fourier series for omega-type monotonic functions. (Chinese)  
    Yu, Guo Hua
    J. Math. Res. Exposition  20  (2000),  no. 1, 97--102, MathSciNet.  
  9. EMG mapping - estimating dipole locations by Legendre polynomial derivatives
    Mirescu, D.; Mathieu, P.A.
    Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings, v 1, 1999, p 580, Compendex.  
  10. Curve offsetting based on Legendre series
    Li, Yong-Ming; Hsu, Vivian Y.
    Computer Aided Geometric Design, v 15, n 7, Jul, 1998, p 711-720, Compendex.  
  11. On the degree of approximation to a function by triangular matrix of its Legendre series.
    Tripathi, L. M.; Tripathi, V. N.; Pandey, S. B.
    Bull. Calcutta Math. Soc. 90 (1998), no. 3, 205--210, MathSciNet.  
  12. Multi-image photometric stereo using surface approximation by Legendre polynomials - Image Understanding
    Kim, Bang-Hwan; Park, Rae-Hong
    Pattern Recognition, 1 August 1998, vol. 31, no. 8, pp. 1033-1047(15), Ingenta.  
  13. Synthesis of unequally spaced linear arrays by Legendre series expansion
    Kumar, B. Preetham; Branner, G.R.
    IEEE Antennas and Propagation Society, AP-S International Symposium (Digest), v 4, 1997, p 2236-2239, Compendex.  
  14. Shape from Shading and Photometric Stereo Using Surface Approximation by Legendre Polynomials
    Kim B.H.; Park R.H.
    Computer Vision and Image Understanding, June 1997, vol. 66, no. 3, pp. 255-270(16), Ingenta.  
  15. Fast training analog approximator on the basis of Legendre polynomials
    Chesnokov, Vyacheslav N.  
    Proceedings of SPIE - The International Society for Optical Engineering, v 3077, 1997, p 382-387, Compendex.  
  16. Recursive Computation of Discrete Legendre Polynomial Coefficients
    Aburdene M.F.
    Multidimensional Systems and Signal Processing, April 1996, vol. 7, no. 2, pp. 221-224(4), Ingenta.
  17. Application of Legendre series to the control problems governed by linear parabolic equations
    Razzaghi M.; Habibi M.
    Mathematics and Computers in Simulation, September 1996, vol. 42, no. 1, pp. 77-84(8), Ingenta.
  18. On the Approximation of Continuous Functions by Fourier-Legendre Sums
    Bashmakova I.; Rafalson S.
    Journal of Approximation Theory, August 1996, vol. 86, no. 2, pp. 197-215(19), Ingenta.
  19. Legendre polynomials of the second kind, Fourier series and Lagrange interpolation
    Mastroianni, G.; Occorsio, D.
    Journal of Computational and Applied Mathematics, 28 November 1996, vol. 75, no. 2, pp. 305-327(23), Compendex.  
  20. Property matrices identification of unbounded medium from unit-impulse response functions using Legendre polynomials: Formulation
    Paronesso, Antonio; Wolf, John P.
    Earthquake Engineering & Structural Dynamics, v 25, n 11, Nov, 1996, p 1231-1245, Compendex.  
  21. Legendre expansion related to the Hubbell Rectangular Source Integral
    Michieli I.; Maksimovic A.
    Radiation Physics and Chemistry, June 1996, vol. 47, no. 6, pp. 779-784(6), Ingenta.  
  22. Fast training analog approximator on the basis of Legendre polynomials
    Chesnokov, Vyacheslav N.  
    Proceedings of International Workshop on Neural Networks for Identification, Control, Robotics, and Signal/Image Processing, NICROSP, 1996, p 299-304, Compendex.  
  23. Minimax approximations to the zeros of Pn(x) and Gauss--Legendre quadrature
    Lether F.G.; Wenston P.R.
    Journal of Computational and Applied Mathematics, 19 May 1995, vol. 59, no. 2, pp. 245-252(8), Ingenta.
  24. Geometrical optics approximation for coefficients of expansion of phase function in Legendre polynomials
    Kokhanovsky, A.A.
    Journal of Aerosol Science, v 26, n Suppl 1, Sep, 1995, p S289, Compendex.  
  25. Approximation of functions of bounded variation by the partial sums of the Legendre-Fourier series. (Chinese)
    Yu, Guo Hua
    J. Hangzhou Univ. Natur. Sci. Ed. 22 (1995), no. 3, 215--221, MathSciNet.  
  26. Muntz Systems and Orthogonal Muntz-Legendre Polynomials  
    Peter Borwein; Tamas Erdelyi; John Zhang  
    Transactions of the American Mathematical Society > Vol. 342, No. 2 (Apr., 1994), pp. 523-542, Jstor.     
  27. Expansions in Legendre polynomials and Lagrange interpolation.  
    Colzani, L.
    Acta Math. Hungar.  61  (1993),  no. 3-4, 289--302, MathSciNet.  
  28. Approximation of linear age-structured population models using legendre polynomials
    Kappel, Franz; Zhang, Kangpei
    Journal of Mathematical Analysis and Applications, v 180, n 2, Dec, 1993, p 518, Compendex.  
  29. The quasi-Fourier-Legendre series and its application to a class of new approximation problems. (Chinese)
    Zhang, Pei Xuan
    Chinese Ann. Math. Ser. A 12 (1991), no. 5, 537--545, MathSciNet.  
  30. Degree of approximation of Hermite-Fejer interpolation based on the zeros of Legendre polynomial and its derivative.
    Zhu, Guo Hua
    Approx. Theory Appl. 6 (1990), no. 1, 32--45, MathSciNet.  
  31. Polynomial and rational approximation to the Legendre function by tau-method.
    Prasad, R. S.; Prasad, Dwarika
    Nepali Math. Sci. Rep. 14 (1989), no. 1-2, 63--71, MathSciNet.  
  32. Lumped and distributed parameter system identification via shifted Legendre polynomials
    Mohan, B.M.; Datta, K.B.
    Journal of Dynamic Systems, Measurement and Control, Transactions ASME, v 110, n 4, Dec, 1988, p 436-440, Compendex.  
  33. Polynomial Nodal Model Using Legendre Expansions  
    Rohach, A. F.  
    Annals of Nuclear Energy, v 13, n 2, 1986, p 57-62, Compendex.  
  34. Some results in the theory of interpolation using the Legendre polynomial and its derivative.  
    Srivastava, K. B.
    J. Approx. Theory  47  (1986),  no. 1, 1--16, MathSciNet.  
  35. Identification Of Time-Varying Bilinear Systems Using Legendre Series  
    Chou, Jyh-Horng; Horng, Ing-Rong  
    Journal of the Franklin Institute, v 322, n 5-6, Nov-Dec, 1986, p 353-359, Compendex.  
  36. Rational and polynomial approximations from Chebyshev and Legendre series for linear differential equations.
    Doha, E. H.
    Arabian J. Sci. Engrg. 10 (1985), no. 1, 3--13, MathSciNet.  
  37. Approximation by polynomials and extension of Parseval's identity for Legendre polynomials to the Lp case.
    Ciesielski, Z.
    Acta Sci. Math. (Szeged) 48 (1985), no. 1-4, 65--70, MathSciNet.  
  38. Optimal Control Of Lumped Parameter Systems Via Shifted Legendre Polynomial Approximation  
    Wang, M. L.; Chang, R. Y.
    Journal of Optimization Theory and Applications, v 45, n 2, Feb, 1985, p 313-324, Compendex.  
  39. Legendre polynomials approximation to dynamic linear state equations with initial or boundary value conditions.
    Chang, Rong Yeu; Wang, Maw Ling
    Internat. J. Control 40 (1984), no. 1, 215--232, MathSciNet.  
  40. On the degree of approximation of Legendre series by a triangular matrix method of summability.
    Mishra, K. N.; Srivastava, R. S. L.
    Bull. Calcutta Math. Soc. 76 (1984), no. 4, 254--261, MathSciNet.  
  41. Divergent Jacobi Polynomial Series  
    Christopher Meaney  
    Proceedings of the American Mathematical Society > Vol. 87, No. 3 (Mar., 1983), pp. 459-462, Jstor.    
  42. On the Weak Behaviour of Partial Sums of Legendre Series  
    S. Chanillo  
    Transactions of the American Mathematical Society > Vol. 268, No. 2 (Dec., 1981), pp. 367-376, Jstor.   
  43. State-Space Approach To Legendre Series Solutions For Linear Systems  
    Naimpally, M.; Naimpally, S.
    Industrial Mathematics, v 31, n pt 1, 1981, p 21-25, Compendex.  
  44. A method for the approximation of a function and its first derivative by Legendre polynomials and its applications. (Russian)
    Peleh, B. L.; Suhorol'ski, M. A.
    Dokl. Akad. Nauk Ukrain. SSR Ser. A No. 3 (1980), 26--29, 90, MathSciNet.  
  45. A Legendre Polynomial Integral  
    James L. Blue  
    Mathematics of Computation > Vol. 33, No. 146 (Apr., 1979), pp. 739-741, Jstor.      
  46. Computation of Legendre series coefficients  
    Robert Piessens  
    Communications of the ACM, Volume 17,  Issue 1  (January 1974), 25.  
  47. On the Uniform Convergence of Fourier-Jacobi Series  
    J. Prasad; H. Hayashi  
    SIAM Journal on Numerical Analysis > Vol. 10, No. 1 (Mar., 1973), pp. 23-27, Jstor.     
  48. The Convergence Almost Everywhere of Legendre Series  
    Harry Pollard  
    Proceedings of the American Mathematical Society > Vol. 35, No. 2 (Oct., 1972), pp. 442-444, Jstor.    
  49. On the Lagrange interpolation based on the zeros of the orthonormal Legendre polynomials.  
    Róna, G.
    Acta Math. Acad. Sci. Hungar.  20  1969 393--397, MathSciNet.  
  50. On Real Singularities of Legendre Expansions  
    Gilbert Walter  
    Proceedings of the American Mathematical Society > Vol. 19, No. 6 (Dec., 1968), pp. 1407-1412, Jstor.    
  51. On the Stability of Midpoint Smoothing with Legendre Polynomials  
    William F. Trench  
    Proceedings of the American Mathematical Society > Vol. 18, No. 2 (Apr., 1967), pp. 191-199, Jstor.     
  52. The use of associated Legendre polynomials for interpolation.  
    Albasiny, E. L.
    Proc. Cambridge Philos. Soc.  57  1961 288--303, MathSciNet.  
  53. Series of Legendre and Laguerre polynomials  
    V. F. Cowling  
    Duke Math. J.  25 (1958), no. 1, 171--176.  
  54. On a Series of Rainville Involving Legendre Polynomials  
    B. R. Bhonsle  
    Proceedings of the American Mathematical Society > Vol. 8, No. 1 (Feb., 1957), pp. 10-14, Jstor.    
  55. Inverse Transforms of Products of Legendre Transforms  
    R. V. Churchill; C. L. Dolph  
    Proceedings of the American Mathematical Society > Vol. 5, No. 1 (Feb., 1954), pp. 93-100, Jstor.   
  56. Note on a Series of Products of Three Legendre Polynomials  
    John P. Vinti  
    Proceedings of the American Mathematical Society > Vol. 2, No. 1 (Feb., 1951), pp. 19-23, Jstor.   
  57. Associated Legendre polynomial approximations.
    Landauer, R.
    J. Appl. Phys. 22, (1951). 87--89, MathSciNet.  
  58. A Property of the Zeros of Legendre Polynomials  
    A. Zygmund  
    Transactions of the American Mathematical Society > Vol. 54, No. 1 (Jul., 1943), pp. 39-56, Jstor.    
  59. On the Absolute Convergence of Polynomial Series  
    Einar Hille  
    The American Mathematical Monthly > Vol. 45, No. 4 (Apr., 1938), pp. 220-226, Jstor.     
  60. Inequalities for the Zeros of Legendre Polynomials and Related Functions  
    Gabriel Szego  
    Transactions of the American Mathematical Society > Vol. 39, No. 1 (Jan., 1936), pp. 1-17, Jstor.      
  61. Series of Orthogonal Polynomials  
    Dunham Jackson  
    The Annals of Mathematics > 2nd Ser., Vol. 34, No. 3 (Jul., 1933), pp. 527-545, Jstor.      
  62. Developments in Legendre Polynomials  
    M. H. Stone  
    The Annals of Mathematics > 2nd Ser., Vol. 27, No. 4 (Jun., 1926), pp. 315-329, Jstor.       
  63. On the Series of Legendre  
    W. H. Young  
    Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 94, No. 660 (Apr., 1918), pp. 292-295, Jstor.  
  64. On the Degree of Convergence of Laplace's Series  
    T. H. Gronwall  
    Transactions of the American Mathematical Society, Vol. 15, No. 1 (Jan., 1914), pp. 1-30, Jstor.   
  65. On the Degree of Convergence of the Development of a Continuous Function According to Legendre's Polynomials  
    Dunham Jackson  
    Transactions of the American Mathematical Society > Vol. 13, No. 3 (Jul., 1912), pp. 305-318, Jstor.    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005