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1: Bibliography B
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Asymptotic expansions for the coefficient functions that arise in turning-point problems.
Proc. Roy. Soc. London Ser. A 410, pp. 35–60.
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More than 41% of the zeros of the zeta function are on the critical line.
Acta Arith. 150 (1), pp. 35–64.
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Numerical calculation of elliptic integrals and elliptic functions. III.
Numer. Math. 13 (4), pp. 305–315.
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Numerical calculation of elliptic integrals and elliptic functions.
Numer. Math. 7 (1), pp. 78–90.
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Numerical calculation of the sine, cosine and Fresnel integrals.
Numer. Math. 9 (5), pp. 380–385.
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2: 14.33 Tables
§14.33 Tables
… ►Zhang and Jin (1996, Chapter 4) tabulates for , , 7D; for , , 8D; for , , 8S; for , , 8D; for , , , , 8S; for , , 8S; for , , , 5D; for , , 7S; for , , 8S. Corresponding values of the derivative of each function are also included, as are 6D values of the first 5 -zeros of and of its derivative for , .
Žurina and Karmazina (1963) tabulates the conical functions for , , 7S; for , , 7S. Auxiliary tables are included to assist computation for larger values of when .
3: 24.20 Tables
§24.20 Tables
… ►Wagstaff (1978) gives complete prime factorizations of and for and , respectively. In Wagstaff (2002) these results are extended to and , respectively, with further complete and partial factorizations listed up to and , respectively. ►For information on tables published before 1961 see Fletcher et al. (1962, v. 1, §4) and Lebedev and Fedorova (1960, Chapters 11 and 14).4: 27.2 Functions
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►Tables of primes (§27.21) reveal great irregularity in their distribution.
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§27.2(ii) Tables
►Table 27.2.1 lists the first 100 prime numbers . Table 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for . ► …5: 24.2 Definitions and Generating Functions
6: 25.10 Zeros
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►More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)).
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7: 26.9 Integer Partitions: Restricted Number and Part Size
8: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
9: Bibliography T
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LSFBTR: A subroutine for calculating spherical Bessel transforms.
Comput. Phys. Comm. 30 (1), pp. 93–99.
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An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives.
J. Comput. Phys. 32 (2), pp. 270–279.
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The numerical computation of the confluent hypergeometric function
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Numer. Math. 41 (1), pp. 63–82.
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Simplified calculation of for positive arguments, and a short table of
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Math. Comp. 22 (102), pp. 448–449.
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Über die Lamésche Differentialgleichung.
Math. Nachr. 30, pp. 137–154 (German).
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10: 3.4 Differentiation
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►For corresponding formulas for second, third, and fourth derivatives, with , see Collatz (1960, Table III, pp. 538–539).
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►The results in this subsection for the partial derivatives follow from Panow (1955, Table 10).
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►For additional formulas involving values of and on square, triangular, and cubic grids, see Collatz (1960, Table VI, pp. 542–546).
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