.%E4%B8%96%E7%95%8C%E6%9D%AF2022%E8%B5%9B%E7%A8%8B%E6%AC%A7%E6%B4%B2%E3%80%8E%E7%BD%91%E5%9D%80%3A68707.vip%E3%80%8F02%E5%B9%B4%E4%B8%96%E7%95%8C%E6%9D%AF%E5%B7%B4%E8%A5%BF%E9%98%9F.b5p6v3-1v5pbd
(0.030 seconds)
11—20 of 707 matching pages
11: 5.13 Integrals
12: 34.5 Basic Properties: Symbol
…
βΊ
34.5.1
βΊ
34.5.2
βΊ
34.5.3
βΊ
34.5.4
…
βΊFor further recursion relations see Varshalovich et al. (1988, §9.6) and Edmonds (1974, pp. 98–99).
…
13: 27.2 Functions
…
βΊ
27.2.9
…
βΊIt is the special case of the function that counts the number of ways of expressing as the product of factors, with the order of factors taken into account.
…Note that .
…
βΊTable 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for .
…
βΊ
14: 7.14 Integrals
…
βΊ
7.14.5
,
…
βΊ
7.14.7
,
…
βΊFor collections of integrals see Apelblat (1983, pp. 131–146), Erdélyi et al. (1954a, vol. 1, pp. 40, 96, 176–177), Geller and Ng (1971), Gradshteyn and Ryzhik (2000, §§5.4 and 6.28–6.32), Marichev (1983, pp. 184–189), Ng and Geller (1969), Oberhettinger (1974, pp. 138–139, 142–143), Oberhettinger (1990, pp. 48–52, 155–158), Oberhettinger and Badii (1973, pp. 171–172, 179–181), Prudnikov et al. (1986b, vol. 2, pp. 30–36, 93–143), Prudnikov et al. (1992a, §§3.7–3.8), and Prudnikov et al. (1992b, §§3.7–3.8).
…
15: Bibliography F
…
βΊ
Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
…
βΊ
Algorithm 309. Gamma function with arbitrary precision.
Comm. ACM 10 (8), pp. 511–512.
…
βΊ
Diffraction of radio waves around the earth’s surface.
Acad. Sci. USSR. J. Phys. 9, pp. 255–266.
…
βΊ
Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface.
J. Acoust. Soc. Amer. 95 (2), pp. 650–660.
…
βΊ
Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions.
In Progress in Optics, E. Wolf (Ed.),
Vol. 9, pp. 311–407.
…
16: 9.8 Modulus and Phase
17: Bibliography B
…
βΊ
The generating function of Jacobi polynomials.
J. London Math. Soc. 13, pp. 8–12.
…
βΊ
Bäcklund transformations and solution hierarchies for the fourth Painlevé equation.
Stud. Appl. Math. 95 (1), pp. 1–71.
…
βΊ
Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces.
J. Phys. A 8 (4), pp. 566–584.
…
βΊ
Asymptotic behavior of the Pollaczek polynomials and their zeros.
Stud. Appl. Math. 96, pp. 307–338.
…
βΊ
Irregular primes and cyclotomic invariants to 12 million.
J. Symbolic Comput. 31 (1-2), pp. 89–96.
…
18: 4.40 Integrals
…
βΊExtensive compendia of indefinite and definite integrals of hyperbolic functions include Apelblat (1983, pp. 96–109), Bierens de Haan (1939), Gröbner and Hofreiter (1949, pp. 139–160), Gröbner and Hofreiter (1950, pp. 160–167), Gradshteyn and Ryzhik (2000, Chapters 2–4), and Prudnikov et al. (1986a, §§1.4, 1.8, 2.4, 2.8).
19: 9.9 Zeros
…
βΊThey lie in the sectors and , and are denoted by , , respectively, in the former sector, and by , , in the conjugate sector, again arranged in ascending order of absolute value (modulus) for See §9.3(ii) for visualizations.
…
βΊ
9.9.6
βΊ
9.9.7
…
βΊ
9.9.10
…
βΊ
9.9.21
…
20: Bibliography J
…
βΊ
Fonctions de Mathieu et fonctions propres de l’oscillateur relativiste.
Ann. Fac. Sci. Toulouse Math. (6) 7 (3), pp. 465–495 (French).
…
βΊ
The birth of the giant component.
Random Structures Algorithms 4 (3), pp. 231–358.
…
βΊ
Numerical calculation of Bessel, Hankel and Airy functions.
Computer Physics Communications 183 (3), pp. 506–519.
…
βΊ
Asymptotic formulas for the zeros of the Meixner polynomials.
J. Approx. Theory 96 (2), pp. 281–300.
…
βΊ
Memoire sur l’itération des fonctions rationnelles.
J. Math. Pures Appl. 8 (1), pp. 47–245 (French).