On a Family of Multivariate Modified Humbert Polynomials

Generating Functions for Special Polynomials and Numbers Including Apostol-type and Humbert-type Polynomials

The aim of this paper is to give generating functions and to prove various properties for some new families of special polynomials and numbers. Several interesting properties of such families and their connections with other polynomials and numbers of the Bernoulli, Euler, Apostol-Bernoulli, ApostolEuler, Genocchi and Fibonacci type are presented. Furthermore, the Fibonacci type polynomials of ...

Some New Results for the Multivariable Humbert Polynomials

In this paper, we present some miscellaneous properties of the multivariable Humbert polynomials whose special cases include some well-known multivariable polynomials such as Chan-Chyan-Srivastava, Lagrange-Hermite and Erkus-Srivastava multivariable polynomials. We give recurrence relations, addition formula and integral representation for them. Then, we obtain some partial differential equatio...

The Matrix Version for the Multivariable Humbert Polynomials

In this paper, the matrix extension of the multivariable Humbert polynomials is introduced. Various families of linear, multilinear and multilateral generating matrix functions of these matrix polynomials are presented. Miscellaneous applications are also discussed. 2000 Mathematics Subject Classification: 33C25; 15A60

On Humbert Humbert’s Mental Disease in Nabokov’s Lolita

On the Tetrahedrally Symmetric Monopole

We study SU(2) BPS monopoles with spectral curves of the form η + χ(ζ + bζ−1) = 0. Previous work has has established a countable family of solutions to Hitchin’s constraint that L was trivial on such a curve. Here we establish that the only curves of this family that yield BPS monopoles correspond to tetrahedrally symmetric monopoles. We introduce several new techniques making use of a factoriz...