Frenzen, C. L., and Wong, R. Uniform asymptotic expansions of Laguerre polynomials. SIAM Journal on Mathematical Analysis 19, 5 (1988), 1232-1248.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... In accordance with the discussion above, we seek a change of variable of the form (44) K(z) t 3 =3 2 t r: 6 As pointed out by a referee, the expansions derived here look similar to uniform asymptotic expansions derived by Wong and his coauthors for Laguerre and Charlier polynomials [9, 26]. 20 C. BANDERIER, P. FLAJOLET, G. SCHAEFFER, AND M. SORIA 3 2 1 0 1 2 3 Re(t) 3 2 1 0 1 2 3 Im(t) 3 2 1 0 1 2 3 3 2 1 0 1 2 3 Re(t) 3 2 1 0 1 2 3 Im(t) 3 2 1 0 1 2 3 Figure 6. The landscape of (f(t) for = 1 and = 0. The parameters = and r = r( ....

Frenzen, C. L., and Wong, R. Uniform asymptotic expansions of Laguerre polynomials. SIAM Journal on Mathematical Analysis 19, 5 (1988), 1232-1248.

.... the phenomenon appears in the integration of exp(nf(t) with a cubic function f , f(t) t 3 3 Gamma 2 t r: 6 As pointed out by a referee, the expansions derived here look similar to uniform asymptotic expansions derived by Wong and his coauthors for Laguerre and Charlier polynomials [9, 26]. 20 C. BANDERIER, P. FLAJOLET, G. SCHAEFFER, AND M. SORIA 3 2 1 0 1 2 3 Re(t) 3 2 1 0 1 2 3 Im(t) 3 2 1 0 1 2 3 3 2 1 0 1 2 3 Re(t) 3 2 1 0 1 2 3 Im(t) 3 2 1 0 1 2 3 Figure 6. The landscape of (f(t) for = 1 and = 0. Indeed, in this case there are two ....

Frenzen, C. L., and Wong, R. Uniform asymptotic expansions of Laguerre polynomials. SIAM Journal on Mathematical Analysis 19, 5 (1988), 1232--1248.

.... 2 where B n are the Bernoulli numbers and RN (z) O 1 z 2N Gamma1 ; z 1; j argzj : Stieltjes showed that: jRN (z)j jB 2N j 2N(2N Gamma 1) 1 cos 2N ( 1 2 ) 1 jzj 2N Gamma1 where = arg z 2 ( Gamma; A proof of this result can also be found in Olver (1974) page 294. 1.2. Bessel functions Stieltjes Th ese de doctorat 2 ) gives several results on Bessel functions, especially the asymptotic expansions of J 0 (x) Y 0 (x) K 0 (x) One has for the ordinary Bessel functions, with = z Gamma ( 1 2 1 4 ) J (z) q 2 z [P ( z) cos Gamma ....

Frenzen, C.L. & R. Wong (1988), Uniform asymptotic expansions of Laguerre polynomials, SIAM J. Math. Anal., 19, 1232--1248.

....is sponsored by the Netherlands Organization for Scientific Research (NWO) CWI is a member of ERCIM, the European Research Consortium for Informatics and Mathematics. Copyright Stichting Mathematisch Centrum P.O. Box 94079, 1090 GB Amsterdam (NL) Kruislaan 413, 1098 SJ Amsterdam (NL) Telephone 31 20 592 9333 Telefax 31 20 592 4199 1 Recent Problems from Uniform Asymptotic Analysis of Integrals In Particular in Connection with Tricomi s Psi GammaFunction Nico M. Temme CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands e mail: nicot cwi.nl URL http: www.cwi.nl nicot ABSTRACT The ....

....Organization for Scientific Research (NWO) CWI is a member of ERCIM, the European Research Consortium for Informatics and Mathematics. Copyright Stichting Mathematisch Centrum P.O. Box 94079, 1090 GB Amsterdam (NL) Kruislaan 413, 1098 SJ Amsterdam (NL) Telephone 31 20 592 9333 Telefax 31 20 592 4199 1 Recent Problems from Uniform Asymptotic Analysis of Integrals In Particular in Connection with Tricomi s Psi GammaFunction Nico M. Temme CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands e mail: nicot cwi.nl URL http: www.cwi.nl nicot ABSTRACT The paper discusses ....

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Frenzen, C.L., & R. Wong (1988). Uniform asymptotic expansions of Laguerre polynomials, SIAM J. Math. Anal., 19, 1232--1248.

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