About the Project

Poisson kernels

AdvancedHelp

(0.001 seconds)

5 matching pages

1: 1.15 Summability Methods
Poisson Kernel
1.15.13 1 2 π 0 2 π P ( r , θ ) d θ = 1 .
1.15.14 P ( r , θ ) 0 ,
1.15.20 A ( r , θ ) = 1 2 π 0 2 π P ( r , θ t ) f ( t ) d t .
Poisson Kernel
2: 18.18 Sums
§18.18(vii) Poisson Kernels
See (18.2.41) for the Poisson kernel in case of general OP’s.
Laguerre
Hermite
For the Poisson kernel of Jacobi polynomials (the Bailey formula) see Bailey (1938). …
3: 18.2 General Orthogonal Polynomials
Poisson kernel
For OP’s p n with h n and orthogonality relation as in (18.2.5) and (18.2.5_5), the Poisson kernel is defined by …Instances where the Poisson kernel is nonnegative are of special interest, see Ismail (2009, Theorem 4.7.12). …
4: 18.12 Generating Functions
See §18.18(vii) for Poisson kernels; these are special cases of bilateral generating functions.
5: Bibliography T
  • C. A. Tracy and H. Widom (1994) Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1), pp. 151–174.
  • C. A. Tracy and H. Widom (1997) On exact solutions to the cylindrical Poisson-Boltzmann equation with applications to polyelectrolytes. Phys. A 244 (1-4), pp. 402–413.