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## 1—10 of 34 matching pages

##### 1: 25.10 Zeros
More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)). …
##### 2: Bibliography B
• A. R. Barnett (1996) The Calculation of Spherical Bessel Functions and Coulomb Functions. In Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions, K. Bartschat and J. Hinze (Eds.), pp. 181–202.
• J. P. Buhler, R. E. Crandall, and R. W. Sompolski (1992) Irregular primes to one million. Math. Comp. 59 (200), pp. 717–722.
• H. M. Bui, B. Conrey, and M. P. Young (2011) More than 41% of the zeros of the zeta function are on the critical line. Acta Arith. 150 (1), pp. 35–64.
• ##### 3: Errata
• Subsection 25.10(ii)

In the paragraph immediately below (25.10.4), it was originally stated that “more than one-third of all zeros in the critical strip lie on the critical line.” which referred to Levinson (1974). This sentence has been updated with “one-third” being replaced with “41%” now referring to Bui et al. (2011) (suggested by Gergő Nemes on 2021-08-23).

• Equation (3.3.34)

In the online version, the leading divided difference operators were previously omitted from these formulas, due to programming error.

Reported by Nico Temme on 2021-06-01

• Table 22.4.3

Originally a minus sign was missing in the entries for $\operatorname{cd}u$ and $\operatorname{dc}u$ in the second column (headed $z+K+iK^{\prime}$). The correct entries are $-k^{-1}\operatorname{ns}z$ and $-k\operatorname{sn}z$. Note: These entries appear online but not in the published print edition. More specifically, Table 22.4.3 in the published print edition is restricted to the three Jacobian elliptic functions $\operatorname{sn},\operatorname{cn},\operatorname{dn}$, whereas Table 22.4.3 covers all 12 Jacobian elliptic functions.

Reported 2014-02-28 by Svante Janson.

• References

Bibliographic citations were added in §§3.5(iv), 4.44, 8.22(ii), 22.4(i), and minor clarifications were made in §§19.12, 20.7(vii), 22.9(i). In addition, several minor improvements were made affecting only ancilliary documents and links in the online version.

• ##### 4: 24.20 Tables
In Wagstaff (2002) these results are extended to $n=60(2)152$ and $n=40(2)88$, respectively, with further complete and partial factorizations listed up to $n=300$ and $n=200$, respectively. …
##### 5: 34.12 Physical Applications
For applications in nuclear structure, see de-Shalit and Talmi (1963); in atomic spectroscopy, see Biedenharn and van Dam (1965, pp. 134–200), Judd (1998), Sobelman (1992, Chapter 4), Shore and Menzel (1968, pp. 268–303), and Wigner (1959); in molecular spectroscopy and chemical reactions, see Burshtein and Temkin (1994, Chapter 5), and Judd (1975). …
##### 6: 27.13 Functions
The exact value of $g\left(k\right)$ is now known for every $k\leq 200,000$. … for all $k\geq 2$, with equality if $4\leq k\leq 200,000$. …
##### 7: Bibliography N
• M. Nardin, W. F. Perger, and A. Bhalla (1992b) Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. J. Comput. Appl. Math. 39 (2), pp. 193–200.
• H. M. Nussenzveig (1992) Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.
• ##### 8: DLMF Project News
error generating summary
##### 9: 8.26 Tables
• Chiccoli et al. (1988) presents a short table of $E_{p}\left(x\right)$ for $p=-\tfrac{9}{2}(1)-\tfrac{1}{2}$, $0\leq x\leq 200$ to 14S.

• ##### 10: Philip J. Davis
Today the DLMF contains close to 600 2D and 3D graphs and more than 200 interactive 3D visualizations. …