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11: 6.13 Zeros
6.13.1 x 0 = 0.37250 74107 81366 63446 19918 66580 .
12: 8.25 Methods of Computation
Expansions involving incomplete gamma functions often require the generation of sequences P ( a + n , x ) , Q ( a + n , x ) , or γ ( a + n , x ) for fixed a and n = 0 , 1 , 2 , . …
13: 5.4 Special Values and Extrema
5.4.6 Γ ( 1 2 ) = π 1 / 2 = 1.77245 38509 05516 02729 ,
5.4.7 Γ ( 1 3 ) = 2.67893 85347 07747 63365 ,
5.4.8 Γ ( 2 3 ) = 1.35411 79394 26400 41694 ,
5.4.9 Γ ( 1 4 ) = 3.62560 99082 21908 31193 ,
5.4.10 Γ ( 3 4 ) = 1.22541 67024 65177 64512 .
14: 17.12 Bailey Pairs
A sequence of pairs of rational functions of several variables ( α n , β n ) , n = 0 , 1 , 2 , , is called a Bailey pair provided that for each n 0 When (17.12.5) is iterated the resulting infinite sequence of Bailey pairs is called a Bailey Chain. …
15: 11.13 Methods of Computation
Sequences of values of 𝐇 ν ( z ) and 𝐋 ν ( z ) , with z fixed, can be computed by application of the inhomogeneous difference equations (11.4.23) and (11.4.25). …
16: Bibliography W
  • E. J. Weniger (1989) Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series. Computer Physics Reports 10 (5-6), pp. 189–371.
  • E. J. Weniger (1996) Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations. Computers in Physics 10 (5), pp. 496–503.
  • J. Wimp (1981) Sequence Transformations and their Applications. Mathematics in Science and Engineering, Vol. 154, Academic Press Inc., New York.
  • 17: 24.15 Related Sequences of Numbers
    §24.15 Related Sequences of Numbers
    18: Bibliography O
  • On-Line Encyclopedia of Integer Sequences (website) OEIS Foundation, Inc., Highland Park, New Jersey.
  • 19: 1.12 Continued Fractions
    b 0 + a 1 b 1 + a 2 b 2 + is equivalent to b 0 + a 1 b 1 + a 2 b 2 + if there is a sequence { d n } n = 0 , d 0 = 1 ,
    d n 0 , such that … A sequence { C n } in the extended complex plane, { } , can be a sequence of convergents of the continued fraction (1.12.3) iff …
    20: 4.2 Definitions
    4.2.11 e = 2.71828 18284 59045 23536
    4.2.17 log 10 e = 0.43429 44819 03251 82765 ,
    4.2.18 ln 10 = 2.30258 50929 94045 68401 .