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21: 5.22 Tables
Abramowitz and Stegun (1964, Chapter 6) tabulates Γ ( x ) , ln Γ ( x ) , ψ ( x ) , and ψ ( x ) for x = 1 ( .005 ) 2 to 10D; ψ ′′ ( x ) and ψ ( 3 ) ( x ) for x = 1 ( .01 ) 2 to 10D; Γ ( n ) , 1 / Γ ( n ) , Γ ( n + 1 2 ) , ψ ( n ) , log 10 Γ ( n ) , log 10 Γ ( n + 1 3 ) , log 10 Γ ( n + 1 2 ) , and log 10 Γ ( n + 2 3 ) for n = 1 ( 1 ) 101 to 8–11S; Γ ( n + 1 ) for n = 100 ( 100 ) 1000 to 20S. Zhang and Jin (1996, pp. 67–69 and 72) tabulates Γ ( x ) , 1 / Γ ( x ) , Γ ( x ) , ln Γ ( x ) , ψ ( x ) , ψ ( x ) , ψ ( x ) , and ψ ( x ) for x = 0 ( .1 ) 5 to 8D or 8S; Γ ( n + 1 ) for n = 0 ( 1 ) 100 ( 10 ) 250 ( 50 ) 500 ( 100 ) 3000 to 51S. …
22: 24.20 Tables
Abramowitz and Stegun (1964, Chapter 23) includes exact values of k = 1 m k n , m = 1 ( 1 ) 100 , n = 1 ( 1 ) 10 ; k = 1 k n , k = 1 ( 1 ) k 1 k n , k = 0 ( 2 k + 1 ) n , n = 1 , 2 , , 20D; k = 0 ( 1 ) k ( 2 k + 1 ) n , n = 1 , 2 , , 18D. …
23: 6.19 Tables
  • Zhang and Jin (1996, pp. 652, 689) includes Si ( x ) , Ci ( x ) , x = 0 ( .5 ) 20 ( 2 ) 30 , 8D; Ei ( x ) , E 1 ( x ) , x = [ 0 , 100 ] , 8S.

  • Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of E 1 ( z ) , ± x = 0.5 , 1 , 3 , 5 , 10 , 15 , 20 , 50 , 100 , y = 0 ( .5 ) 1 ( 1 ) 5 ( 5 ) 30 , 50 , 100 , 8S.

  • 24: 8.26 Tables
  • Zhang and Jin (1996, Table 3.8) tabulates γ ( a , x ) for a = 0.5 , 1 , 3 , 5 , 10 , 25 , 50 , 100 , x = 0 ( .1 ) 1 ( 1 ) 3 , 5 ( 5 ) 30 , 50 , 100 to 8D or 8S.

  • Zhang and Jin (1996, Table 19.1) tabulates E n ( x ) for n = 1 , 2 , 3 , 5 , 10 , 15 , 20 , x = 0 ( .1 ) 1 , 1.5 , 2 , 3 , 5 , 10 , 20 , 30 , 50 , 100 to 7D or 8S.

  • 25: 10.75 Tables
  • Zhang and Jin (1996, pp. 185–195) tabulates J n ( x ) , J n ( x ) , Y n ( x ) , Y n ( x ) , n = 0 ( 1 ) 10 ( 10 ) 50 , 100 , x = 1 , 5, 10, 25, 50, 100, 9S; J n + α ( x ) , J n + α ( x ) , Y n + α ( x ) , Y n + α ( x ) , n = 0 ( 1 ) 5 , 10 , 30 , 50 , 100 , α = 1 4 , 1 3 , 1 2 , 2 3 , 3 4 , x = 1 , 5 , 10 , 50 , 8S; real and imaginary parts of J n + α ( z ) , J n + α ( z ) , Y n + α ( z ) , Y n + α ( z ) , n = 0 ( 1 ) 15 , 20 ( 10 ) 50 , 100 , α = 0 , 1 2 , z = 4 + 2 i , 20 + 10 i , 8S.

  • Morgenthaler and Reismann (1963) tabulates j n , m for n = 21 ( 1 ) 51 and j n , m < 100 , 7-10S.

  • Döring (1971) tabulates the first 100 values of ν ( > 1 ) for which J ν ( x ) has the double zero x = ν , 10D.

  • Zhang and Jin (1996, pp. 240–250) tabulates I n ( x ) , I n ( x ) , K n ( x ) , K n ( x ) , n = 0 ( 1 ) 10 ( 10 ) 50 , 100 , x = 1 , 5 , 10 , 25 , 50 , 100 , 9S; I n + α ( x ) , I n + α ( x ) , K n + α ( x ) , K n + α ( x ) , n = 0 ( 1 ) 5 , 10, 30, 50, 100, α = 1 4 , 1 3 , 1 2 , 2 3 , 3 4 , x = 1 , 5, 10, 50, 8S; real and imaginary parts of I n + α ( z ) , I n + α ( z ) , K n + α ( z ) , K n + α ( z ) , n = 0 ( 1 ) 15 , 20(10)50, 100, α = 0 , 1 2 , z = 4 + 2 i , 20 + 10 i , 8S.

  • The main tables in Abramowitz and Stegun (1964, Chapter 10) give 𝗃 n ( x ) , 𝗒 n ( x ) n = 0 ( 1 ) 8 , x = 0 ( .1 ) 10 , 5–8S; 𝗃 n ( x ) , 𝗒 n ( x ) n = 0 ( 1 ) 20 ( 10 ) 50 , 100, x = 1 , 2 , 5 , 10 , 50 , 100 , 10S; 𝗂 n ( 1 ) ( x ) , 𝗄 n ( x ) , n = 0 , 1 , 2 , x = 0 ( .1 ) 5 , 4–9D; 𝗂 n ( 1 ) ( x ) , 𝗄 n ( x ) , n = 0 ( 1 ) 20 ( 10 ) 50 , 100, x = 1 , 2 , 5 , 10 , 50 , 100 , 10S. (For the notation see §10.1 and §10.47(ii).)

  • 26: 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.

  • 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.

  • 27: 11.14 Tables
  • Agrest et al. (1982) tabulates 𝐇 n ( x ) and e x 𝐋 n ( x ) for n = 0 , 1 and x = 0 ( .001 ) 5 ( .005 ) 15 ( .01 ) 100 to 11D.

  • Barrett (1964) tabulates 𝐋 n ( x ) for n = 0 , 1 and x = 0.2 ( .005 ) 4 ( .05 ) 10 ( .1 ) 19.2 to 5 or 6S, x = 6 ( .25 ) 59.5 ( .5 ) 100 to 2S.

  • 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.

  • 28: Charles W. Clark
    Clark received the R&D 100 Award, Distinguished Presidential Rank Award of the U. …
    29: 28.35 Tables
  • National Bureau of Standards (1967) includes the eigenvalues a n ( q ) , b n ( q ) for n = 0 ( 1 ) 3 with q = 0 ( .2 ) 20 ( .5 ) 37 ( 1 ) 100 , and n = 4 ( 1 ) 15 with q = 0 ( 2 ) 100 ; Fourier coefficients for ce n ( x , q ) and se n ( x , q ) for n = 0 ( 1 ) 15 , n = 1 ( 1 ) 15 , respectively, and various values of q in the interval [ 0 , 100 ] ; joining factors g e , n ( q ) , f e , n ( q ) for n = 0 ( 1 ) 15 with q = 0 ( .5  to  10 ) 100 (but in a different notation). Also, eigenvalues for large values of q . Precision is generally 8D.

  • Blanch and Clemm (1969) includes eigenvalues a n ( q ) , b n ( q ) for q = ρ e i ϕ , ρ = 0 ( .5 ) 25 , ϕ = 5 ( 5 ) 90 , n = 0 ( 1 ) 15 ; 4D. Also a n ( q ) and b n ( q ) for q = i ρ , ρ = 0 ( .5 ) 100 , n = 0 ( 2 ) 14 and n = 2 ( 2 ) 16 , respectively; 8D. Double points for n = 0 ( 1 ) 15 ; 8D. Graphs are included.

  • 30: 27.21 Tables
    Lehmer (1914) lists all primes up to 100 06721. …