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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
Laguerre
Hermite
These Poisson kernels are positive, provided that x , y are real, 0 z < 1 , and in the case of (18.18.27) x , y 0 . …
3: 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.