About the Project
NIST

金肯职业技术学院毕业证制作【言正 微aptao168】0oB4ifw

AdvancedHelp

The terms "ob4ifw", "aptao168" were not found.Possible alternative term: "caption".

(0.004 seconds)

1—10 of 693 matching pages

1: 33.24 Tables
  • Abramowitz and Stegun (1964, Chapter 14) tabulates F 0 ( η , ρ ) , G 0 ( η , ρ ) , F 0 ( η , ρ ) , and G 0 ( η , ρ ) for η = 0.5 ( .5 ) 20 and ρ = 1 ( 1 ) 20 , 5S; C 0 ( η ) for η = 0 ( .05 ) 3 , 6S.

  • Curtis (1964a) tabulates P ( ϵ , r ) , Q ( ϵ , r ) 33.1), and related functions for = 0 , 1 , 2 and ϵ = - 2 ( .2 ) 2 , with x = 0 ( .1 ) 4 for ϵ < 0 and x = 0 ( .1 ) 10 for ϵ 0 ; 6D.

  • 2: 26.15 Permutations: Matrix Notation
    The set 𝔖 n 26.13) can be identified with the set of n × n matrices of 0’s and 1’s with exactly one 1 in each row and column. The permutation σ corresponds to the matrix in which there is a 1 at the intersection of row j with column σ ( j ) , and 0’s in all other positions. … Define r 0 ( B ) = 1 . … The Ferrers board of shape ( b 1 , b 2 , , b n ) , 0 b 1 b 2 b n , is the set B = { ( j , k ) |  1 j n , 1 k b j } . …If B is the Ferrers board of shape ( 0 , 1 , 2 , , n - 1 ) , then …
    3: 24.2 Definitions and Generating Functions
    B 2 n + 1 = 0 ,
    ( - 1 ) n + 1 B 2 n > 0 , n = 1 , 2 , .
    E 2 n + 1 = 0 ,
    ( - 1 ) n E 2 n > 0 .
    E ~ n ( x ) = E n ( x ) , 0 x < 1 ,
    4: 11.14 Tables
  • Abramowitz and Stegun (1964, Chapter 12) tabulates H n ( x ) , H n ( x ) - Y n ( x ) , and I n ( x ) - L n ( x ) for n = 0 , 1 and x = 0 ( .1 ) 5 , x - 1 = 0 ( .01 ) 0.2 to 6D or 7D.

  • Abramowitz and Stegun (1964, Chapter 12) tabulates 0 x ( I 0 ( t ) - L 0 ( t ) ) d t and ( 2 / π ) x t - 1 H 0 ( t ) d t for x = 0 ( .1 ) 5 to 5D or 7D; 0 x ( H 0 ( t ) - Y 0 ( t ) ) d t - ( 2 / π ) ln x , 0 x ( I 0 ( t ) - L 0 ( t ) ) d t - ( 2 / π ) ln x , and x t - 1 ( H 0 ( t ) - Y 0 ( t ) ) d t for x - 1 = 0 ( .01 ) 0.2 to 6D.

  • Agrest et al. (1982) tabulates 0 x H 0 ( t ) d t and e - x 0 x L 0 ( t ) d t for x = 0 ( .001 ) 5 ( .005 ) 15 ( .01 ) 100 to 11D.

  • Jahnke and Emde (1945) tabulates E n ( x ) for n = 1 , 2 and x = 0 ( .01 ) 14.99 to 4D.

  • Agrest and Maksimov (1971, Chapter 11) defines incomplete Struve, Anger, and Weber functions and includes tables of an incomplete Struve function H n ( x , α ) for n = 0 , 1 , x = 0 ( .2 ) 10 , and α = 0 ( .2 ) 1.4 , 1 2 π , together with surface plots.

  • 5: 20.4 Values at z = 0
    §20.4 Values at z = 0
    20.4.1 θ 1 ( 0 , q ) = θ 2 ( 0 , q ) = θ 3 ( 0 , q ) = θ 4 ( 0 , q ) = 0 ,
    20.4.6 θ 1 ( 0 , q ) = θ 2 ( 0 , q ) θ 3 ( 0 , q ) θ 4 ( 0 , q ) .
    20.4.7 θ 1 ′′ ( 0 , q ) = θ 2 ′′′ ( 0 , q ) = θ 3 ′′′ ( 0 , q ) = θ 4 ′′′ ( 0 , q ) = 0 .
    20.4.12 θ 1 ′′′ ( 0 , q ) θ 1 ( 0 , q ) = θ 2 ′′ ( 0 , q ) θ 2 ( 0 , q ) + θ 3 ′′ ( 0 , q ) θ 3 ( 0 , q ) + θ 4 ′′ ( 0 , q ) θ 4 ( 0 , q ) .
    6: 4.31 Special Values and Limits
    Table 4.31.1: Hyperbolic functions: values at multiples of 1 2 π i .
    z 0 1 2 π i π i 3 2 π i
    cosh z 1 0 - 1 0
    coth z 0 0 1
    4.31.1 lim z 0 sinh z z = 1 ,
    4.31.2 lim z 0 tanh z z = 1 ,
    4.31.3 lim z 0 cosh z - 1 z 2 = 1 2 .
    7: 32.4 Isomonodromy Problems
    32.4.4 A ( z , λ ) = ( 4 λ 4 + 2 w 2 + z ) [ 1 0 0 - 1 ] - i ( 4 λ 2 w + 2 w 2 + z ) [ 0 - i i 0 ] - ( 2 λ w + 1 2 λ ) [ 0 1 1 0 ] ,
    32.4.12 z v 0 = 2 v 0 u 1 v 1 + v 0 + ( u 0 ( 2 v 0 - z ) / v 1 ) ,
    If w = - u 0 / ( v 0 v 1 ) , then …where
    32.4.16 θ 0 = 4 v 0 z ( θ ( 1 - z 4 v 0 ) + z - 2 v 0 2 v 0 v 1 u 0 + u 1 v 1 ) .
    8: 14.33 Tables
  • Abramowitz and Stegun (1964, Chapter 8) tabulates P n ( x ) for n = 0 ( 1 ) 3 , 9 , 10 , x = 0 ( .01 ) 1 , 5–8D; P n ( x ) for n = 1 ( 1 ) 4 , 9 , 10 , x = 0 ( .01 ) 1 , 5–7D; Q n ( x ) and Q n ( x ) for n = 0 ( 1 ) 3 , 9 , 10 , x = 0 ( .01 ) 1 , 6–8D; P n ( x ) and P n ( x ) for n = 0 ( 1 ) 5 , 9 , 10 , x = 1 ( .2 ) 10 , 6S; Q n ( x ) and Q n ( x ) for n = 0 ( 1 ) 3 , 9 , 10 , x = 1 ( .2 ) 10 , 6S. (Here primes denote derivatives with respect to x .)

  • Zhang and Jin (1996, Chapter 4) tabulates P n ( x ) for n = 2 ( 1 ) 5 , 10 , x = 0 ( .1 ) 1 , 7D; P n ( cos θ ) for n = 1 ( 1 ) 4 , 10 , θ = 0 ( 5 ) 90 , 8D; Q n ( x ) for n = 0 ( 1 ) 2 , 10 , x = 0 ( .1 ) 0.9 , 8S; Q n ( cos θ ) for n = 0 ( 1 ) 3 , 10 , θ = 0 ( 5 ) 90 , 8D; P n m ( x ) for m = 1 ( 1 ) 4 , n - m = 0 ( 1 ) 2 , n = 10 , x = 0 , 0.5 , 8S; Q n m ( x ) for m = 1 ( 1 ) 4 , n = 0 ( 1 ) 2 , 10 , 8S; P ν m ( cos θ ) for m = 0 ( 1 ) 3 , ν = 0 ( .25 ) 5 , θ = 0 ( 15 ) 90 , 5D; P n ( x ) for n = 2 ( 1 ) 5 , 10 , x = 1 ( 1 ) 10 , 7S; Q n ( x ) for n = 0 ( 1 ) 2 , 10 , x = 2 ( 1 ) 10 , 8S. Corresponding values of the derivative of each function are also included, as are 6D values of the first 5 ν -zeros of P ν m ( cos θ ) and of its derivative for m = 0 ( 1 ) 4 , θ = 10 , 30 , 150 .

  • Belousov (1962) tabulates P n m ( cos θ ) (normalized) for m = 0 ( 1 ) 36 , n - m = 0 ( 1 ) 56 , θ = 0 ( 2.5 ) 90 , 6D.

  • Žurina and Karmazina (1964, 1965) tabulate the conical functions P - 1 2 + i τ ( x ) for τ = 0 ( .01 ) 50 , x = - 0.9 ( .1 ) 0.9 , 7S; P - 1 2 + i τ ( x ) for τ = 0 ( .01 ) 50 , x = 1.1 ( .1 ) 2 ( .2 ) 5 ( .5 ) 10 ( 10 ) 60 , 7D. Auxiliary tables are included to facilitate computation for larger values of τ when - 1 < x < 1 .

  • Žurina and Karmazina (1963) tabulates the conical functions P - 1 2 + i τ 1 ( x ) for τ = 0 ( .01 ) 25 , x = - 0.9 ( .1 ) 0.9 , 7S; P - 1 2 + i τ 1 ( x ) for τ = 0 ( .01 ) 25 , x = 1.1 ( .1 ) 2 ( .2 ) 5 ( .5 ) 10 ( 10 ) 60 , 7S. Auxiliary tables are included to assist computation for larger values of τ when - 1 < x < 1 .

  • 9: 15.15 Sums
    15.15.1 F ( a , b c ; 1 z ) = ( 1 - z 0 z ) - a s = 0 ( a ) s s ! F ( - s , b c ; 1 z 0 ) ( 1 - z z 0 ) - s .
    Here z 0 ( 0 ) is an arbitrary complex constant and the expansion converges when | z - z 0 | > max ( | z 0 | , | z 0 - 1 | ) . …
    10: 11.15 Approximations
  • Luke (1975, pp. 416–421) gives Chebyshev-series expansions for H n ( x ) , L n ( x ) , 0 | x | 8 , and H n ( x ) - Y n ( x ) , x 8 , for n = 0 , 1 ; 0 x t - m H 0 ( t ) d t , 0 x t - m L 0 ( t ) d t , 0 | x | 8 , m = 0 , 1 and 0 x ( H 0 ( t ) - Y 0 ( t ) ) d t , x t - 1 ( H 0 ( t ) - Y 0 ( t ) ) d t , x 8 ; the coefficients are to 20D.

  • MacLeod (1993) gives Chebyshev-series expansions for L 0 ( x ) , L 1 ( x ) , 0 x 16 , and I 0 ( x ) - L 0 ( x ) , I 1 ( x ) - L 1 ( x ) , x 16 ; the coefficients are to 20D.

  • Newman (1984) gives polynomial approximations for H n ( x ) for n = 0 , 1 , 0 x 3 , and rational-fraction approximations for H n ( x ) - Y n ( x ) for n = 0 , 1 , x 3 . The maximum errors do not exceed 1.2×10⁻⁸ for the former and 2.5×10⁻⁸ for the latter.