Poisson kernel ♦ 3 matching pages ♦ SearchAdvancedHelp (0.001 seconds) 3 matching pages 1: 1.15 Summability Methods … ► Poisson Kernel … ► 1.15.13 1 2 π ∫ 0 2 π P ( r , θ ) d θ = 1 . ⓘ Symbols: π : the ratio of the circumference of a circle to its diameter, d x : differential, ∫ : integral and P ( r , θ ) : Poisson kernel Permalink: http://dlmf.nist.gov/1.15.E13 Encodings: pMML, png, TeX See also: Annotations for §1.15(iii), §1.15(iii), §1.15 and Ch.1 … ► 1.15.14 P ( r , θ ) → 0 , ⓘ Symbols: P ( r , θ ) : Poisson kernel Permalink: http://dlmf.nist.gov/1.15.E14 Encodings: pMML, png, TeX See also: Annotations for §1.15(iii), §1.15(iii), §1.15 and Ch.1 … ► 1.15.20 A ( r , θ ) = 1 2 π ∫ 0 2 π P ( r , θ - t ) f ( t ) d t . ⓘ Symbols: π : the ratio of the circumference of a circle to its diameter, d x : differential, ∫ : integral, P ( r , θ ) : Poisson kernel and A ( r , θ ) : Abel mean Permalink: http://dlmf.nist.gov/1.15.E20 Encodings: pMML, png, TeX See also: Annotations for §1.15(iii), §1.15(iii), §1.15 and Ch.1 … ► 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. ⓘ External Links: ISSN 0010-3616, FullText, MathReview (Estelle L. Basor), ZentralBlatt Referenced by: §32.14. Encodings: BibTeX ► 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. ⓘ External Links: ISSN 0378-4371, Document, MathReview (Vitor R. Vieira) Referenced by: §32.11(iv). Encodings: BibTeX …