Approximations for zeros of Hermite functions

A novel process is provided for producing a nucleoside, such as cytarabine, or a nucleoside analogue, comprising the step of reacting 2,2'-O-cyclonucleoside or an analogue thereof with an amine. Preferably, the process is conducted in the presence of an aqueous solvent. A novel process for the production of the precursor 2,2'-O-cyclonucleoside compounds and pharmaceutically acceptable salts thereof is also provided which comprises reacting a 2,3'-O-diaikylstannylene nucleoside compound with an amine in the presence of a sulfonyl compound. Cytarabine is a known antineoplastic and antiviral agent.

[1]  G. Szegő Zeros of orthogonal polynomials , 1939 .

[2]  F. W. J. Olver,et al.  A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  T. MacRobert Higher Transcendental Functions , 1955, Nature.

[4]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[5]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[6]  Eugene P. Wigner,et al.  Formulas and Theorems for the Special Functions of Mathematical Physics , 1966 .

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

[8]  L. Durand Nicholson-Type Integrals for Products of Gegenbauer Functions and Related Topics , 1975 .

[9]  W. Hayman,et al.  17.—An Upper Bound for the Largest Zero of Hermite's Function with Applications to Subharmonic Functions , 1976, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[10]  L. Durand Product Formulas and Nicholson-Type Integrals for Jacobi Functions. I: Summary of Results , 1978 .

[11]  C. M. Place,et al.  Ordinary Differential Equations , 1982 .

[12]  Improving the Asymptotics for the Greatest Zeros of Hermite Polynomials , 1995 .

[13]  Asymptotics for the Greatest Zeros of Szegö's Generalization of the Hermite Polynomials , 1997 .

[14]  M. E. Muldoon,et al.  Inequalities and monotonicity properties for zeros of Hermite functions , 1999, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[15]  Árpád Elbert,et al.  Some recent results on the zeros of Bessel functions and orthogonal polynomials , 2001 .

[16]  A Nicholson-Type Integral for the Product of Two Parabolic Cylinder Functions D ν ( x ) D ν (− x ) AT ℜν≪0 , 2003 .

[17]  Martin E. Muldoon,et al.  Continuous ranking of zeros of special functions , 2008 .