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1: 26.21 Tables
Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts ± 2 ( mod 5 ) , partitions into parts ± 1 ( mod 5 ) , and unrestricted plane partitions up to 100. … Goldberg et al. (1976) contains tables of binomial coefficients to n = 100 and Stirling numbers to n = 40 .
2: 12.19 Tables
  • Abramowitz and Stegun (1964, Chapter 19) includes U ( a , x ) and V ( a , x ) for ± a = 0 ( .1 ) 1 ( .5 ) 5 , x = 0 ( .1 ) 5 , 5S; W ( a , ± x ) for ± a = 0 ( .1 ) 1 ( 1 ) 5 , x = 0 ( .1 ) 5 , 4-5D or 4-5S.

  • Kireyeva and Karpov (1961) includes D p ( x ( 1 + i ) ) for ± x = 0 ( .1 ) 5 , p = 0 ( .1 ) 2 , and ± x = 5 ( .01 ) 10 , p = 0 ( .5 ) 2 , 7D.

  • Karpov and Čistova (1964) includes D p ( x ) for p = 2 ( .1 ) 0 , ± x = 0 ( .01 ) 5 ; p = 2 ( .05 ) 0 , ± x = 5 ( .01 ) 10 , 6D.

  • Zhang and Jin (1996, pp. 455–473) includes U ( ± n 1 2 , x ) , V ( ± n 1 2 , x ) , U ( ± ν 1 2 , x ) , V ( ± ν 1 2 , x ) , and derivatives, ν = n + 1 2 , n = 0 ( 1 ) 10 ( 10 ) 30 , x = 0.5 , 1 , 5 , 10 , 30 , 50 , 8S; W ( a , ± x ) , W ( a , ± x ) , and derivatives, a = h ( 1 ) 5 + h , x = 0.5 , 1 and a = h ( 1 ) 5 + h , x = 5 , h = 0 , 0.5 , 8S. Also, first zeros of U ( a , x ) , V ( a , x ) , and of derivatives, a = 6 ( .5 ) 1 , 6D; first three zeros of W ( a , x ) and of derivative, a = 0 ( .5 ) 4 , 6D; first three zeros of W ( a , ± x ) and of derivative, a = 0.5 ( .5 ) 5.5 , 6D; real and imaginary parts of U ( a , z ) , a = 1.5 ( 1 ) 1.5 , z = x + i y , x = 0.5 , 1 , 5 , 10 , y = 0 ( .5 ) 10 , 8S.

  • 3: 11.8 Analogs to Kelvin Functions
    §11.8 Analogs to Kelvin Functions
    For properties of Struve functions of argument x e ± 3 π i / 4 see McLachlan and Meyers (1936).
    4: 4.16 Elementary Properties
    Table 4.16.2: Trigonometric functions: quarter periods and change of sign.
    x θ 1 2 π ± θ π ± θ 3 2 π ± θ 2 π ± θ
    sin x sin θ cos θ sin θ cos θ ± sin θ
    cos x cos θ sin θ cos θ ± sin θ cos θ
    tan x tan θ cot θ ± tan θ cot θ ± tan θ
    cot x cot θ tan θ ± cot θ tan θ ± cot θ
    5: 28.25 Asymptotic Expansions for Large z
    28.25.1 M ν ( 3 , 4 ) ( z , h ) e ± i ( 2 h cosh z ( 1 2 ν + 1 4 ) π ) ( π h ( cosh z + 1 ) ) 1 2 m = 0 D m ± ( 4 i h ( cosh z + 1 ) ) m ,
    D 1 ± = 0 ,
    D 0 ± = 1 ,
    28.25.3 ( m + 1 ) D m + 1 ± + ( ( m + 1 2 ) 2 ± ( m + 1 4 ) 8 i h + 2 h 2 a ) D m ± ± ( m 1 2 ) ( 8 i h m ) D m 1 ± = 0 , m 0 .
    6: 4.13 Lambert W -Function
    The decreasing solution can be identified as W ± 1 ( x 0 i ) . … W 0 ( z ) is a single-valued analytic function on ( , e 1 ] , real-valued when z > e 1 , and has a square root branch point at z = e 1 . …The other branches W k ( z ) are single-valued analytic functions on ( , 0 ] , have a logarithmic branch point at z = 0 , and, in the case k = ± 1 , have a square root branch point at z = e 1 0 i respectively. … and has several advantages over the Lambert W -function (see Lawrence et al. (2012)), and the tree T -function T ( z ) = W ( z ) , which is a solution of … where t 0 for W 0 , t 0 for W ± 1 on the relevant branch cuts, …
    7: 36.7 Zeros
    x m , n ± = 2 y m ( 2 n + 1 2 + ( 1 ) m 1 2 ± 1 4 ) π , m = 1 , 2 , 3 , , n = 0 , ± 1 , ± 2 , .
    Table 36.7.1: Zeros of cusp diffraction catastrophe to 5D. …
    Zeros { x y } inside, and zeros [ x y ] outside, the cusp x 2 = 8 27 | y | 3 .
    { ± 0.52768 4.37804 } [ ± 2.35218 1.74360 ]
    { ± 1.41101 5.55470 } { ± 2.36094 5.52321 } [ ± 4.42707 3.05791 ]
    { ± 0.38488 8.31916 } { ± 2.71193 8.22315 } { ± 3.49286 8.20326 } { ± 5.96669 7.85723 } { ± 6.79538 7.80456 } [ ± 9.17308 5.55831 ]
    x n = ± ( 8 27 ) 1 / 2 | y n | 3 / 2 ( 1 + ξ n ) ,
    8: 7.23 Tables
  • Zhang and Jin (1996, pp. 637, 639) includes ( 2 / π ) e x 2 , erf x , x = 0 ( .02 ) 1 ( .04 ) 3 , 8D; C ( x ) , S ( x ) , x = 0 ( .2 ) 10 ( 2 ) 100 ( 100 ) 500 , 8D.

  • Zhang and Jin (1996, pp. 638, 640–641) includes the real and imaginary parts of erf z , x [ 0 , 5 ] , y = 0.5 ( .5 ) 3 , 7D and 8D, respectively; the real and imaginary parts of x e ± i t 2 d t , ( 1 / π ) e i ( x 2 + ( π / 4 ) ) x e ± i t 2 d t , x = 0 ( .5 ) 20 ( 1 ) 25 , 8D, together with the corresponding modulus and phase to 8D and 6D (degrees), respectively.

  • Fettis et al. (1973) gives the first 100 zeros of erf z and w ( z ) (the table on page 406 of this reference is for w ( z ) , not for erfc z ), 11S.

  • 9: Charles W. Clark
    He has been a Visiting Fellow at the Australian National University, a Dr. Lee Fellow at Christ Church College of the University of Oxford, and Visiting Professor at the National University of Singapore. Clark received the R&D 100 Award, Distinguished Presidential Rank Award of the U. …
    10: 6.4 Analytic Continuation
    6.4.4 Ci ( z e ± π i ) = ± π i + Ci ( z ) ,
    6.4.5 Chi ( z e ± π i ) = ± π i + Chi ( z ) ,
    6.4.6 f ( z e ± π i ) = π e i z f ( z ) ,
    6.4.7 g ( z e ± π i ) = π i e i z + g ( z ) .