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test function space


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1: 1.16 Distributions
The linear space of all test functions with the above definition of convergence is called a test function space. … … The space 𝒯 ( ) of test functions for tempered distributions consists of all infinitely-differentiable functions such that the function and all its derivatives are O ( | x | - N ) as | x | for all N . … For tempered distributions the space of test functions 𝒯 n is the set of all infinitely-differentiable functions ϕ of n variables that satisfy …Tempered distributions are continuous linear functionals on this space of test functions. …
2: Software Index
Open Source With Book Commercial
4.48(v) Testing
‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support. … In the list below we identify four main sources of software for computing special functions. …
  • Commercial Software.

    Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.

  • The following are web-based software repositories with significant holdings in the area of special functions. …
    3: Bibliography G
  • A. Gervois and H. Navelet (1985a) Integrals of three Bessel functions and Legendre functions. I. J. Math. Phys. 26 (4), pp. 633–644.
  • A. Gervois and H. Navelet (1985b) Integrals of three Bessel functions and Legendre functions. II. J. Math. Phys. 26 (4), pp. 645–655.
  • S. Goldstein (1927) Mathieu functions. Trans. Camb. Philos. Soc. 23, pp. 303–336.
  • P. Groeneboom and D. R. Truax (2000) A monotonicity property of the power function of multivariate tests. Indag. Math. (N.S.) 11 (2), pp. 209–218.
  • K. I. Gross and D. St. P. Richards (1991) Hypergeometric functions on complex matrix space. Bull. Amer. Math. Soc. (N.S.) 24 (2), pp. 349–355.
  • 4: Bibliography B
  • H. F. Baker (1995) Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions. Cambridge University Press, Cambridge.
  • M. V. Berry and F. J. Wright (1980) Phase-space projection identities for diffraction catastrophes. J. Phys. A 13 (1), pp. 149–160.
  • D. K. Bhaumik and S. K. Sarkar (2002) On the power function of the likelihood ratio test for MANOVA. J. Multivariate Anal. 82 (2), pp. 416–421.
  • W. Bosma and M.-P. van der Hulst (1990) Faster Primality Testing. In Advances in Cryptology—EUROCRYPT ’89 Proceedings, J.-J. Quisquater and J. Vandewalle (Eds.), Lecture Notes in Computer Science, Vol. 434, New York, pp. 652–656.
  • D. M. Bressoud (1989) Factorization and Primality Testing. Springer-Verlag, New York.
  • 5: 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.
  • F. Marcellán, M. Alfaro, and M. L. Rezola (1993) Orthogonal polynomials on Sobolev spaces: Old and new directions. J. Comput. Appl. Math. 48 (1-2), pp. 113–131.
  • 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.