About the Project

test functions


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11—20 of 24 matching pages

11: DLMF Project News
error generating summary
12: David M. Bressoud
Bressoud has published numerous papers in number theory, combinatorics, and special functions. … 227, in 1980, Factorization and Primality Testing, published by Springer-Verlag in 1989, Second Year Calculus from Celestial Mechanics to Special Relativity, published by Springer-Verlag in 1992, A Radical Approach to Real Analysis, published by the Mathematical Association of America in 1994, with a second edition in 2007, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, published by the Mathematical Association of America and Cambridge University Press in 1999, A Course in Computational Number Theory (with S. … Bressoud served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions.
13: 1.10 Functions of a Complex Variable
Analytic Functions
§1.10(vi) Multivalued Functions
§1.10(vii) Inverse Functions
M -test
M -test
14: Philip J. Davis
After being asked by Milton Abramowitz to work on the project, he chose to write the Chapter “Gamma Function and Related Functions. … Olver had been recruited to write the Chapter “Bessel Functions of Integer Order” for A&S by Milton Abramowitz, who passed away suddenly in 1958. … This immediately led to discussions among some of the project members about what might be possible, and the discovery that some interactive graphics work had already been done for the NIST Matrix Market, a publicly available repository of test matrices for comparing the effectiveness of numerical linear algebra algorithms. … DLMF users can rotate, rescale, zoom and otherwise explore mathematical function surfaces. The surface color map can be changed from height-based to phase-based for complex valued functions, and density plots can be generated through strategic scaling. …
15: Bibliography P
  • E. Pairman (1919) Tables of Digamma and Trigamma Functions. In Tracts for Computers, No. 1, K. Pearson (Ed.),
  • R. B. Paris (2002c) Exponential asymptotics of the Mittag-Leffler function. Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
  • K. Pearson (Ed.) (1968) Tables of the Incomplete Beta-function. 2nd edition, Published for the Biometrika Trustees at the Cambridge University Press, Cambridge.
  • M. D. Perlman and I. Olkin (1980) Unbiasedness of invariant tests for MANOVA and other multivariate problems. Ann. Statist. 8 (6), pp. 1326–1341.
  • Prime Pages (website)
  • 16: Bibliography M
  • I. G. Macdonald (1990) Hypergeometric Functions.
  • A. J. MacLeod (1996b) Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.
  • B. Markman (1965) Contribution no. 14. The Riemann zeta function. BIT 5, pp. 138–141.
  • N. W. McLachlan (1934) Loud Speakers: Theory, Performance, Testing and Design. Oxford University Press, New York.
  • J. Morris (1969) Algorithm 346: F-test probabilities [S14]. Comm. ACM 12 (3), pp. 184–185.
  • 17: Bibliography N
  • A. Nakamura (1996) Toda equation and its solutions in special functions. J. Phys. Soc. Japan 65 (6), pp. 1589–1597.
  • E. Neuman (2013) Inequalities and bounds for the incomplete gamma function. Results Math. 63 (3-4), pp. 1209–1214.
  • E. H. Neville (1951) Jacobian Elliptic Functions. 2nd edition, Clarendon Press, Oxford.
  • N. E. Nørlund (1955) Hypergeometric functions. Acta Math. 94, pp. 289–349.
  • Number Theory Web (website)
  • 18: Bibliography E
  • ECMNET Project (website)
  • H. M. Edwards (1974) Riemann’s Zeta Function. Academic Press, New York-London.
  • E. Elizalde (1995) Ten Physical Applications of Spectral Zeta Functions. Lecture Notes in Physics. New Series m: Monographs, Vol. 35, Springer-Verlag, Berlin.
  • A. Erdélyi (1941b) On Lamé functions. Philos. Mag. (7) 31, pp. 123–130.
  • A. Erdélyi (1941c) On algebraic Lamé functions. Philos. Mag. (7) 32, pp. 348–350.
  • 19: 27.12 Asymptotic Formulas: Primes
    27.12.2 p n > n ln n , n = 1 , 2 , .
    where λ ( α ) depends only on α , and ϕ ( m ) is the Euler totient function27.2). … For current records see The Great Internet Mersenne Prime Search. A pseudoprime test is a test that correctly identifies most composite numbers. …Descriptions and comparisons of pseudoprime tests are given in Bressoud and Wagon (2000, §§2.4, 4.2, and 8.2) and Crandall and Pomerance (2005, §§3.4–3.6). …
    20: Bibliography K
  • S. L. Kalla (1992) On the evaluation of the Gauss hypergeometric function. C. R. Acad. Bulgare Sci. 45 (6), pp. 35–36.
  • R. P. Kanwal (1983) Generalized functions. Mathematics in Science and Engineering, Vol. 171, Academic Press, Inc., Orlando, FL.
  • K. S. Kölbig (1970) Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function. Math. Comp. 24 (111), pp. 679–696.
  • K. S. Kölbig (1972c) Programs for computing the logarithm of the gamma function, and the digamma function, for complex argument. Comput. Phys. Comm. 4, pp. 221–226.
  • M. D. Kruskal and P. A. Clarkson (1992) The Painlevé-Kowalevski and poly-Painlevé tests for integrability. Stud. Appl. Math. 86 (2), pp. 87–165.