About the Project

by%20reflection

AdvancedHelp

(0.002 seconds)

4 matching pages

1: 26.9 Integer Partitions: Restricted Number and Part Size
β–Ί
Table 26.9.1: Partitions p k ⁑ ( n ) .
β–Ί β–Ίβ–Ίβ–Ί
n k
8 0 1 5 10 15 18 20 21 22 22 22
β–Ί
β–ΊThe conjugate partition is obtained by reflecting the Ferrers graph across the main diagonal or, equivalently, by representing each integer by a column of dots. …
2: 10.75 Tables
β–Ί
  • Achenbach (1986) tabulates J 0 ⁑ ( x ) , J 1 ⁑ ( x ) , Y 0 ⁑ ( x ) , Y 1 ⁑ ( x ) , x = 0 ⁒ ( .1 ) ⁒ 8 , 20D or 18–20S.

  • β–Ί
  • MacDonald (1989) tabulates the first 30 zeros, in ascending order of absolute value in the fourth quadrant, of the function J 0 ⁑ ( z ) i ⁒ J 1 ⁑ ( z ) , 6D. (Other zeros of this function can be obtained by reflection in the imaginary axis).

  • β–Ί
  • Bickley et al. (1952) tabulates x n ⁒ I n ⁑ ( x ) or e x ⁒ I n ⁑ ( x ) , x n ⁒ K n ⁑ ( x ) or e x ⁒ K n ⁑ ( x ) , n = 2 ⁒ ( 1 ) ⁒ 20 , x = 0 (.01 or .1) 10(.1) 20, 8S; I n ⁑ ( x ) , K n ⁑ ( x ) , n = 0 ⁒ ( 1 ) ⁒ 20 , x = 0 or 0.1 ⁒ ( .1 ) ⁒ 20 , 10S.

  • β–Ί
  • Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of K n ⁑ ( z ) and K n ⁑ ( z ) , for n = 2 ⁒ ( 1 ) ⁒ 20 , 9S.

  • β–Ί
  • Zhang and Jin (1996, p. 322) tabulates ber ⁑ x , ber ⁑ x , bei ⁑ x , bei ⁑ x , ker ⁑ x , ker ⁑ x , kei ⁑ x , kei ⁑ x , x = 0 ⁒ ( 1 ) ⁒ 20 , 7S.

  • 3: 36.5 Stokes Sets
    β–Ί
    36.5.4 80 ⁒ x 5 40 ⁒ x 4 55 ⁒ x 3 + 5 ⁒ x 2 + 20 ⁒ x 1 = 0 ,
    β–Ί
    36.5.7 X = 9 20 + 20 ⁒ u 4 Y 2 20 ⁒ u 2 + 6 ⁒ u 2 ⁒ sign ⁑ ( z ) ,
    β–ΊOne of the sheets is symmetrical under reflection in the plane y = 0 , and is given by …
    4: Bibliography D
    β–Ί
  • C. de la Vallée Poussin (1896a) Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction ΞΆ ⁒ ( s ) de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann. Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
  • β–Ί
  • C. de la Vallée Poussin (1896b) Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire M ⁒ x + N . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
  • β–Ί
  • B. Döring (1966) Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.
  • β–Ί
  • B. Dubrovin and M. Mazzocco (2000) Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (1), pp. 55–147.
  • β–Ί
  • T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.