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The generating function is also used to express a number of integrals involving the LFG polynomials as finite sums of parabolic cylinder functions.” 91g:33012 33C45 41A10 41A60 Sharapudinov, I. ... For details about the above hypergeometric 33 SPECIAL FUNCTIONS 3706 family of polynomials a good reference would be to a book by T. S. ...
Parabolic Cylinder Functions, Hermite Polynomials, and Gauss-Hermite Quadrature The parabolic cylinder functions are given by where H N () are the Hermite polynomials. ... The plan for the rest of this paper is the following: first, basic properties of parabolic cylinder functions, Hermite polynomials, and Gauss-Hermite quadrature are reviewed, which are necessary for the ... This research of A.M. is partially supported by grants from the National Science Foundation and the Office of Naval Research. B.K. is supported as a postdoctoral fellow through these grants. ...doi:10.1073/pnas.98.4.1341 pmid:11171952 pmcid:PMC29258 fatcat:5dlq2tcsize7hlho4tli4wqlie
Parabolic Cylinder Functions, Hermite Polynomials, and Gauss-Hermite Quadrature The parabolic cylinder functions are given by where H N () are the Hermite polynomials. ... The plan for the rest of this paper is the following: first, basic properties of parabolic cylinder functions, Hermite polynomials, and Gauss-Hermite quadrature are reviewed, which are necessary for the ... This research of A.M. is partially supported by grants from the National Science Foundation and the Office of Naval Research. B.K. is supported as a postdoctoral fellow through these grants. ...doi:10.1073/pnas.041583698 pmid:11171952 pmcid:PMC29258 fatcat:h7zv53f6p5cp5dj6ugb7mc6uha
We present a new method for the interpolation of given data points and associated normals with surface parametric patches with rational normal fields. ... Our construction is based on the isotropic model of the dual space to which the original data are pushed. ... We thank to all referees for their valuable comments, which helped us to improve the paper. ...arXiv:1602.01224v2 fatcat:27sqblroifbmhn3svpdwhhhkx4
Specifically, a nonlinear superposition principle for PIV, hierarchies of solutions expressible in terms of complementary error or parabolic cylinder functions as well as rational solutions will be derived ... A suitable factorisation of (2) facilitates the identification of a number of solutions which take the form of ratios of two polynomials in the variable z_n and the limits of these solutions yield rational ... In addition he is grateful to the staff and students of New College, UNSW for their provision of a Visiting Fellowship and to the School of Mathematics for their hospitality. ...arXiv:solv-int/9412002v1 fatcat:r2lpt5xmy5fbxb2tbokudp2xg4
, we derive a dependence on Hermite polynomials and error functions.” ... L. 87c:34004 Functions on a parabolic cylinder with a negative integer index. (Russian) Differentsial'nye Uravneniya 21 (1985), no. 11, 2001-2003, 2024. ...
Many special functions are amenable to this analysis, and we give several examples of application: modified Bessel functions, parabolic cylinder functions, Legendre functions of imaginary variable and ... are sharp both as a function of n and x. ... functions (see Section 4.1.2 for the case of parabolic cylinder functions). ...doi:10.1186/1029-242x-2012-65 fatcat:3gcup6lfibhordqyqcctufkfsa
Nuclear Associates. Circle 666. program. ESS operates on VAX and UNIX computers and workstations. New MethodsResearch. Circle 533. ... , Euler, Debye, and Spence), exponential integral and related functions (including cosine and sine integrals and hyperbolic extensions, Fresnel integrals, and parabolic cylinder functions), periodic functions ...doi:10.1126/science.238.4833.1597 pmid:17784302 fatcat:tevonn5vuvhxlplp5d4xxqgkni
In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit. ... Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on S^m, for all m≥ 3. ... The associated eigenfunctions are the Hermite polynomials h k (σ). ...doi:10.1088/0951-7715/24/8/007 fatcat:b32wlcbowveuhbwn3tf3nnfexe
We merge these two points of view to get a new and efficient method to obtain integrals of special functions and the summation of the associated generating functions as well. ... Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. ... Acknowledgements The work of Dr. S. Licciardi was supported by an Enea Research Center individual fellowship. Author Contributions ...arXiv:1908.04160v1 fatcat:7szretfsf5djpddjuz34ox7eya
Physics Letters A
A suitable factorisation of (1) facilitates the identification of a number of solutions which take the form of ratios of two polynomials in the variable z_n. ... It is also known that there exist exact solutions of PIV (2) that are expressible in terms of the complementary error function and in this article we show that a discrete analogue of this function can ... In addition he is grateful to the staff and students of New College, UNSW for their provision of a Visiting Fellowship and to the School of Mathematics for their hospitality. ...doi:10.1016/0375-9601(94)91294-7 fatcat:vuodrsmfvjfjzptuqyhd76ppv4
will become new members of the community of special functions". ... Further representations are given of the associated special polynomials in terms of Schur functions. ... A family of τ -functions In this section we give a description of some of the rational solutions of the symmetric A (1) 2n system (1.1) in terms of the Schur functions. ...doi:10.1111/j.1467-9590.2008.00410.x fatcat:7fqbieo7cvckzn4zbe5fwc4d3q
We construct a class of generalized nonlinear coherent states by means of a newly obtained class of 2D complex orthogonal polynomials. The associated coherent states transform is discussed. ... We illustrate this construction with the example of the measure r^β e^-rdr, which leads to a new generalization of the true-polyanalytic Bargmann transform. ... + 1) −1 |D −β (ix √ 2)| −2 dx where D a (•) is the parabolic cylinder function. ...arXiv:1812.11620v1 fatcat:kmefovj4f5awtecpclsp3oejo4
The validity of the method depends on one's ability to transform a given differential equation to its simplest possible form, so a program must be executed that involves transformations of both variables ... We derive a new criterion for deducing the intervals of oscillatory behavior in the solutions of ordinary second-order linear homogeneous differential equations from their coefficients. ... First form of the parabolic cylinder equation We call the equation where n is a constant , the first form of the parabolic cylinder differential equation. ...doi:10.1186/s13662-016-0774-x fatcat:vkd4ibglnnfv3do3hietmejnha
In this paper the structure of the roots of these special polynomials, and the special polynomials associated with algebraic solutions of the third and fifth Painlevé equations, is studied and it is shown ... Rational solutions of the second, third and fourth Painlevé equations (P II -P IV ) can be expressed in terms of logarithmic derivatives of special polynomials that are defined through coupled second order ... expressible in terms of parabolic cylinder functions D ν (ξ), or a special case of the Whittaker functions M κ,µ (ζ) and W κ,µ (ζ) (cf ...doi:10.1007/bf03321618 fatcat:6kp4ohmfi5haho2pmnl44ny2ne
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