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Page 3706 of Mathematical Reviews Vol. , Issue 91G
[page]

1991
*
Mathematical Reviews
*

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. ...##
###
A numerical strategy for efficient modeling of the equatorial wave guide

2001
*
Proceedings of the National Academy of Sciences of the United States of America
*

*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. ...

##
###
A numerical strategy for efficient modeling of the equatorial wave guide

2001
*
Proceedings of the National Academy of Sciences of the United States of America
*

*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. ...

##
###
Smooth surface interpolation using patches with rational offsets
[article]

2016
*
arXiv
*
pre-print

We present

arXiv:1602.01224v2
fatcat:27sqblroifbmhn3svpdwhhhkx4
*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. ...##
###
Backlund Transformations and Hierarchies of Exact Solutions for the Fourth Painleve Equation and their Application to Discrete Equations
[article]

1994
*
arXiv
*
pre-print

Specifically,

arXiv:solv-int/9412002v1
fatcat:r2lpt5xmy5fbxb2tbokudp2xg4
*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. ...##
###
Page 1285 of Mathematical Reviews Vol. , Issue 87c
[page]

1987
*
Mathematical Reviews
*

, 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. ...##
###
On bounds for solutions of monotonic first order difference-differential systems

2012
*
Journal of Inequalities and Applications
*

Many special

doi:10.1186/1029-242x-2012-65
fatcat:3gcup6lfibhordqyqcctufkfsa
*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*). ...##
###
Products & Materials

1987
*
Science
*

Nuclear

doi:10.1126/science.238.4833.1597
pmid:17784302
fatcat:tevonn5vuvhxlplp5d4xxqgkni
*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*...##
###
Formal matched asymptotics for degenerate Ricci flow neckpinches

2011
*
Nonlinearity
*

In this paper, we describe and provide plausibility arguments for

doi:10.1088/0951-7715/24/8/007
fatcat:b32wlcbowveuhbwn3tf3nnfexe
*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). ...##
###
Operational vs. Umbral Methods and Borel Transform
[article]

2019
*
arXiv
*
pre-print

We merge these two points

arXiv:1908.04160v1
fatcat:7szretfsf5djpddjuz34ox7eya
*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 ...##
###
New exact solutions of the discrete fourth Painleve´equation

1994
*
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. ...

##
###
The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials

2008
*
Studies in applied mathematics (Cambridge)
*

will become

doi:10.1111/j.1467-9590.2008.00410.x
fatcat:7fqbieo7cvckzn4zbe5fwc4d3q
*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*. ...##
###
Nonlinear coherent states associated with a measure on the positive real half line
[article]

2018
*
arXiv
*
pre-print

We construct

arXiv:1812.11620v1
fatcat:kmefovj4f5awtecpclsp3oejo4
*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*. ...##
###
A program for predicting the intervals of oscillations in the solutions of ordinary second-order linear homogeneous differential equations

2016
*
Advances in Difference Equations
*

The validity

doi:10.1186/s13662-016-0774-x
fatcat:vkd4ibglnnfv3do3hietmejnha
*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. ...##
###
Special Polynomials Associated with Rational Solutions of the Painlevé Equations and Applications to Soliton Equations

2006
*
Computational methods in Function Theory
*

In this paper the structure

doi:10.1007/bf03321618
fatcat:6kp4ohmfi5haho2pmnl44ny2ne
*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 ...
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