On the Approximation of the Jacobi Polynomials
Uri Elias and Harry Gingold
Source: Rocky Mountain J. Math. Volume 37, Number 1 (2007), 159-184.
First Page PDF: View first page of article (PDF, 74 KB)Primary Subjects: 33C45
Secondary Subjects: 34E10
Keywords: Jacobi polynomials; special functions; hypergeometric equation; asymptotic approximations
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1181069323
Digital Object Identifier: doi:10.1216/rmjm/1181069323
Mathematical Reviews number (MathSciNet):
MR2316441
Zentralblatt MATH identifier:
05249866
References
R.A. Askey, Orthogonal polynomials and special functions, Soc. for Industrial and Appl. Math. (SIAM), Philadelphia, 1975.
Mathematical Reviews (MathSciNet):
MR481145
H.A. Carteret, M.E.H. Ismail and B. Richmond, Three routes to the exact asymptotics for the one-dimensional quantum walk, J. Phys. A 36 (2003), 8775-8795.
Mathematical Reviews (MathSciNet):
MR2008667
Zentralblatt MATH:
1049.82025
Digital Object Identifier: doi:10.1088/0305-4470/36/33/305
H. Gingold, An invariant asymptotic formula for solutions of second order ODE's, Asymptot. Anal. 1 (1988), 309-325.
Mathematical Reviews (MathSciNet):
MR972304
--------, Approximations of solutions of $y^\pp= \phi(x, \varepsilon)y$ with several points and moving singularities, Asymptot. Anal. 6 (1993), 335-364.
Mathematical Reviews (MathSciNet):
MR1203624
Zentralblatt MATH:
0780.34041
--------, Global and uniform approximations for solutions of the modified Bessel equation, Dyn. Contin. Discrete Impuls. Syst. 5 (1999), 405-414.
Mathematical Reviews (MathSciNet):
MR1678266
W.A. Harris, Jr. and D. Lutz, On the asymptotic integration of linear differential systems, J. Math. Anal. Appl. 48 (1974), 1-16.
Mathematical Reviews (MathSciNet):
MR355222
Zentralblatt MATH:
0304.34043
Digital Object Identifier: doi:10.1016/0022-247X(74)90211-X
--------, A unified theory of asymptotic integration, J. Math. Anal. Appl. 57 (1977), 571-586.
Mathematical Reviews (MathSciNet):
MR430436
Zentralblatt MATH:
0398.34012
Digital Object Identifier: doi:10.1016/0022-247X(77)90247-5
N.N. Lebedev, Special functions and their applications, Dover, New York, 1972.
Mathematical Reviews (MathSciNet):
MR350075
Jos L. López and Nico M. Temme, Approximation of orthogonal polynomials in terms of Hermite polynomials (Dedicated to Richard A. Askey on the occasion of his 65th birthday), Part II, Methods Appl. Anal. 6 (1999), 131-146.
Mathematical Reviews (MathSciNet):
MR1803886
F.W.J. Olver, Asymptotics and special functions, Academic Press, New York, 1974.
Mathematical Reviews (MathSciNet):
MR435697
--------, Whittaker functions with both parameters large: Uniform approximations in terms of parabolic functions, Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), 213-234.
Mathematical Reviews (MathSciNet):
MR592550
G. Szegö, On some Hamiltonian forms associated with two given curves on the complex plane, Trans. Amer. Math. Soc. 40 (1936), 450-461.
Mathematical Reviews (MathSciNet):
MR1501884
Zentralblatt MATH:
0015.34603
Digital Object Identifier: doi:10.2307/1989634
JSTOR: links.jstor.org
--------, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Providence, RI, 1975.
Nico M. Temme, Polynomial asymptotic estimates of Gegenbauer, Laguerre, and Jacobi polynomials, in Asymptotic and computational analysis (R. Wong, ed.), Lecture Notes in Pure and Appl. Math., vol. 124, Dekker, New York, 1990, pp. 455-476.
Mathematical Reviews (MathSciNet):
MR1052447
Zentralblatt MATH:
0704.33009
--------, Special functions: An introduction to the classical functions of mathematical physics, Wiley-Interscience, New York, 1996.
Mathematical Reviews (MathSciNet):
MR1376370
W. Van Assche, Asymptotics for orthogonal polynomials, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet):
MR903848
W.R. Wasow, Asymptotic expansions for ordinary differential equations, John Wiley, New York, 1965.
H. Widom and H. Wilf, Small eigenvalues of large Hankel matrices, Proc. Amer. Math. Soc. 17 (1966), 338-344.
Mathematical Reviews (MathSciNet):
MR189237
Zentralblatt MATH:
0168.28102
Digital Object Identifier: doi:10.2307/2035162
JSTOR: links.jstor.org
Rocky Mountain Journal of Mathematics