About the Project

.币安法国球队网址『世界杯佣金分红55%,咨询专员:@ky975』.uiq.k2q1w9-2022年11月29日1时52分6秒maooc00kk

AdvancedHelp

Did you mean .币安法国球队网址『世界杯佣金分红55%,咨询专员:@1975』.uiq.k2q1w9-2022年11月29日1时52分6秒maooc00kk ?

(0.005 seconds)

1—10 of 305 matching pages

1: 34.4 Definition: 6 j Symbol
§34.4 Definition: 6 j Symbol
The 6 j symbol is defined by the following double sum of products of 3 j symbols: … The 6 j symbol can be expressed as the finite sum … where F 3 4 is defined as in §16.2. For alternative expressions for the 6 j symbol, written either as a finite sum or as other terminating generalized hypergeometric series F 3 4 of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).
2: 25.20 Approximations
  • Cody et al. (1971) gives rational approximations for ζ ( s ) in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are 0.5 s 5 , 5 s 11 , 11 s 25 , 25 s 55 . Precision is varied, with a maximum of 20S.

  • 3: Mathematical Introduction
    The NIST Handbook has essentially the same objective as the Handbook of Mathematical Functions that was issued in 1964 by the National Bureau of Standards as Number 55 in the NBS Applied Mathematics Series (AMS). … As a consequence, in addition to providing more information about the special functions that were covered in AMS 55, the NIST Handbook includes several special functions that have appeared in the interim in applied mathematics, the physical sciences, and engineering, as well as in other areas. See, for example, Chapters 16, 17, 18, 19, 21, 27, 29, 31, 32, 34, 35, and 36. Two other ways in which this Handbook differs from AMS 55, and other handbooks, are as follows. … For equations or other technical information that appeared previously in AMS 55, the DLMF usually includes the corresponding AMS 55 equation number, or other form of reference, together with corrections, if needed. …
    4: 28.6 Expansions for Small q
    Leading terms of the power series for a m ( q ) and b m ( q ) for m 6 are: …
    28.6.2 a 1 ( q ) = 1 + q 1 8 q 2 1 64 q 3 1 1536 q 4 + 11 36864 q 5 + 49 5 89824 q 6 + 55 94 37184 q 7 83 353 89440 q 8 + ,
    28.6.3 b 1 ( q ) = 1 q 1 8 q 2 + 1 64 q 3 1 1536 q 4 11 36864 q 5 + 49 5 89824 q 6 55 94 37184 q 7 83 353 89440 q 8 + ,
    28.6.10 a 5 ( q ) = 25 + 1 48 q 2 + 11 7 74144 q 4 + 1 1 47456 q 5 + 37 8918 13888 q 6 + ,
    28.6.11 b 5 ( q ) = 25 + 1 48 q 2 + 11 7 74144 q 4 1 1 47456 q 5 + 37 8918 13888 q 6 + ,
    5: 6.14 Integrals
    For collections of integrals, see Apelblat (1983, pp. 110–123), Bierens de Haan (1939, pp. 373–374, 409, 479, 571–572, 637, 664–673, 680–682, 685–697), Erdélyi et al. (1954a, vol. 1, pp. 40–42, 96–98, 177–178, 325), Geller and Ng (1969), Gradshteyn and Ryzhik (2000, §§5.2–5.3 and 6.2–6.27), Marichev (1983, pp. 182–184), Nielsen (1906b), Oberhettinger (1974, pp. 139–141), Oberhettinger (1990, pp. 53–55 and 158–160), Oberhettinger and Badii (1973, pp. 172–179), Prudnikov et al. (1986b, vol. 2, pp. 24–29 and 64–92), Prudnikov et al. (1992a, §§3.4–3.6), Prudnikov et al. (1992b, §§3.4–3.6), and Watrasiewicz (1967).
    6: Bibliography H
  • J. R. Herndon (1961a) Algorithm 55: Complete elliptic integral of the first kind. Comm. ACM 4 (4), pp. 180.
  • D. R. Herrick and S. O’Connor (1998) Inverse virial symmetry of diatomic potential curves. J. Chem. Phys. 109 (1), pp. 11–19.
  • H. W. Hethcote (1970) Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems. J. Mathematical Phys. 11 (8), pp. 2501–2504.
  • K. Horata (1989) An explicit formula for Bernoulli numbers. Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.
  • C. Hunter (1981) Two Parametric Eigenvalue Problems of Differential Equations. In Spectral Theory of Differential Operators (Birmingham, AL, 1981), North-Holland Math. Stud., Vol. 55, pp. 233–241.
  • 7: 10.12 Generating Function and Associated Series
    10.12.4 1 = J 0 ( z ) + 2 J 2 ( z ) + 2 J 4 ( z ) + 2 J 6 ( z ) + ,
    cos z = J 0 ( z ) 2 J 2 ( z ) + 2 J 4 ( z ) 2 J 6 ( z ) + ,
    1 2 z sin z = 4 J 2 ( z ) 16 J 4 ( z ) + 36 J 6 ( z ) .
    8: 24.2 Definitions and Generating Functions
    Table 24.2.5: Coefficients b n , k of the Bernoulli polynomials B n ( x ) = k = 0 n b n , k x k .
    k
    n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    11 0 5 6 0 11 2 0 11 0 11 0 55 6 11 2 1
    12 691 2730 0 5 0 33 2 0 22 0 33 2 0 11 6 1
    Table 24.2.6: Coefficients e n , k of the Euler polynomials E n ( x ) = k = 0 n e n , k x k .
    k
    n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
    12 0 2073 0 3410 0 1683 0 396 0 55 0 6 1
    9: Bibliography E
  • C. Eckart (1930) The penetration of a potential barrier by electrons. Phys. Rev. 35 (11), pp. 1303–1309.
  • A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi (1953b) Higher Transcendental Functions. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.
  • F. H. L. Essler, H. Frahm, A. R. Its, and V. E. Korepin (1996) Painlevé transcendent describes quantum correlation function of the X X Z antiferromagnet away from the free-fermion point. J. Phys. A 29 (17), pp. 5619–5626.
  • L. Euler (1768) Institutiones Calculi Integralis. Opera Omnia (1), Vol. 11, pp. 110–113.
  • G. A. Evans and J. R. Webster (1999) A comparison of some methods for the evaluation of highly oscillatory integrals. J. Comput. Appl. Math. 112 (1-2), pp. 55–69.
  • 10: Bibliography F
  • M. V. Fedoryuk (1991) Asymptotics of the spectrum of the Heun equation and of Heun functions. Izv. Akad. Nauk SSSR Ser. Mat. 55 (3), pp. 631–646 (Russian).
  • N. Fleury and A. Turbiner (1994) Polynomial relations in the Heisenberg algebra. J. Math. Phys. 35 (11), pp. 6144–6149.
  • A. S. Fokas and M. J. Ablowitz (1982) On a unified approach to transformations and elementary solutions of Painlevé equations. J. Math. Phys. 23 (11), pp. 2033–2042.
  • P. J. Forrester and N. S. Witte (2002) Application of the τ -function theory of Painlevé equations to random matrices: P V , P III , the LUE, JUE, and CUE. Comm. Pure Appl. Math. 55 (6), pp. 679–727.
  • L. W. Fullerton (1972) Algorithm 435: Modified incomplete gamma function. Comm. ACM 15 (11), pp. 993–995.