论文信息 - Full length article: Asymptotics for Ménage polynomials and certain hypergeometric polynomials of type 3F1

Full length article: Asymptotics for Ménage polynomials and certain hypergeometric polynomials of type 3F1

Using a uniform version of Laplace's method, strong asymptotics for suitably normalized Menage polynomials and certain hypergeometric polynomials of type "3F"1 are established. Moreover, weak asymptotics and further properties of the zeros are derived.

Thorsten Neuschel | Thorsten Neuschel

[1] Thorsten Neuschel. A uniform version of Laplace´s method for contour integrals , 2012 .

[2] H. Srivastava,et al. Asymptotic distributions of the zeros of a family of hypergeometric polynomials , 2012 .

[3] C. W. Clenshaw,et al. The special functions and their approximations , 1972 .

[4] F. Olver. Asymptotics and Special Functions , 1974 .

[5] John Riordan,et al. Introduction to Combinatorial Analysis , 1958 .

[6] John Riordan,et al. Introduction to Combinatorial Analysis , 1959 .

[7] Ronald F. Boisvert,et al. NIST Handbook of Mathematical Functions , 2010 .

[8] Arno B. J. Kuijlaars,et al. Riemann-Hilbert Analysis for Laguerre Polynomials with Large Negative Parameter , 2001 .

[9] E. Saff,et al. Logarithmic Potentials with External Fields , 1997, Grundlehren der mathematischen Wissenschaften.

[10] Hans-Peter Blatt,et al. Discrepancy of Signed Measures and Polynomial Approximation , 2001 .

[11] M. Ismail,et al. Classical and Quantum Orthogonal Polynomials in One Variable: Bibliography , 2005 .

[12] G. Szegö,et al. Bemerkungen zu einem Satz von J. H. Grace über die Wurzeln algebraischer Gleichungen , 1922 .

[13] Richard Askey,et al. Permutation Problems and Special Functions , 1976, Canadian Journal of Mathematics.

[14] Rene F. Swarttouw,et al. Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.