About the Project

large ell

AdvancedHelp

(0.003 seconds)

1—10 of 36 matching pages

1: Bibliography F
  • C. Ferreira, J. L. López, and E. Pérez Sinusía (2013a) The third Appell function for one large variable. J. Approx. Theory 165, pp. 60–69.
  • C. Ferreira, J. L. López, and E. P. Sinusía (2013b) The second Appell function for one large variable. Mediterr. J. Math. 10 (4), pp. 1853–1865.
  • J. L. Fields (1973) Uniform asymptotic expansions of certain classes of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.
  • J. L. Fields (1983) Uniform asymptotic expansions of a class of Meijer G -functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.
  • L. Fox (1960) Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments. National Physical Laboratory Mathematical Tables, Vol. 4. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
  • 2: Bibliography L
  • J. L. López and P. J. Pagola (2010) The confluent hypergeometric functions M ( a , b ; z ) and U ( a , b ; z ) for large b and z . J. Comput. Appl. Math. 233 (6), pp. 1570–1576.
  • J. L. López, P. Pagola, and E. Pérez Sinusía (2013a) Asymptotics of the first Appell function F 1 with large parameters II. Integral Transforms Spec. Funct. 24 (12), pp. 982–999.
  • J. L. López, P. Pagola, and E. Pérez Sinusía (2013b) Asymptotics of the first Appell function F 1 with large parameters. Integral Transforms Spec. Funct. 24 (9), pp. 715–733.
  • J. L. López (1999) Asymptotic expansions of the Whittaker functions for large order parameter. Methods Appl. Anal. 6 (2), pp. 249–256.
  • J. L. López and N. M. Temme (2010b) Large degree asymptotics of generalized Bernoulli and Euler polynomials. J. Math. Anal. Appl. 363 (1), pp. 197–208.
  • 3: Bibliography U
  • F. Ursell (1972) Integrals with a large parameter. Several nearly coincident saddle-points. Proc. Cambridge Philos. Soc. 72, pp. 49–65.
  • 4: Bibliography B
  • L. Baker (1992) C Mathematical Function Handbook. McGraw-Hill, Inc., New York.
  • L. C. Biedenharn, R. L. Gluckstern, M. H. Hull, and G. Breit (1955) Coulomb functions for large charges and small velocities. Phys. Rev. (2) 97 (2), pp. 542–554.
  • G. Blanch and I. Rhodes (1955) Table of characteristic values of Mathieu’s equation for large values of the parameter. J. Washington Acad. Sci. 45 (6), pp. 166–196.
  • 5: Bibliography K
  • U. J. Knottnerus (1960) Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters. J. B. Wolters, Groningen.
  • 6: Bibliography O
  • A. B. Olde Daalhuis (2003a) Uniform asymptotic expansions for hypergeometric functions with large parameters. I. Analysis and Applications (Singapore) 1 (1), pp. 111–120.
  • A. B. Olde Daalhuis (2003b) Uniform asymptotic expansions for hypergeometric functions with large parameters. II. Analysis and Applications (Singapore) 1 (1), pp. 121–128.
  • A. B. Olde Daalhuis (2010) Uniform asymptotic expansions for hypergeometric functions with large parameters. III. Analysis and Applications (Singapore) 8 (2), pp. 199–210.
  • F. W. J. Olver (1952) Some new asymptotic expansions for Bessel functions of large orders. Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.
  • F. W. J. Olver (1962) Tables for Bessel Functions of Moderate or Large Orders. National Physical Laboratory Mathematical Tables, Vol. 6. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
  • 7: 11.13 Methods of Computation
    Then from the limiting forms for small argument (§§11.2(i), 10.7(i), 10.30(i)), limiting forms for large argument (§§11.6(i), 10.7(ii), 10.30(ii)), and the connection formulas (11.2.5) and (11.2.6), it is seen that 𝐇 ν ( x ) and 𝐋 ν ( x ) can be computed in a stable manner by integrating forwards, that is, from the origin toward infinity. …
    8: Bibliography C
  • F. Calogero (1978) Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial L n α ( x )  as the index α  and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials. Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.
  • 9: 10.45 Functions of Imaginary Order
    In consequence of (10.45.5)–(10.45.7), I ~ ν ( x ) and K ~ ν ( x ) comprise a numerically satisfactory pair of solutions of (10.45.1) when x is large, and either I ~ ν ( x ) and ( 1 / π ) sinh ( π ν ) K ~ ν ( x ) , or I ~ ν ( x ) and K ~ ν ( x ) , comprise a numerically satisfactory pair when x is small, depending whether ν 0 or ν = 0 . … For properties of I ~ ν ( x ) and K ~ ν ( x ) , including uniform asymptotic expansions for large ν and zeros, see Dunster (1990a). In this reference I ~ ν ( x ) is denoted by ( 1 / π ) sinh ( π ν ) L i ν ( x ) . …
    10: 34.8 Approximations for Large Parameters
    §34.8 Approximations for Large Parameters
    For large values of the parameters in the 3 j , 6 j , and 9 j symbols, different asymptotic forms are obtained depending on which parameters are large. …
    34.8.1 { j 1 j 2 j 3 j 2 j 1 l 3 } = ( 1 ) j 1 + j 2 + j 3 + l 3 ( 4 π ( 2 j 1 + 1 ) ( 2 j 2 + 1 ) ( 2 l 3 + 1 ) sin θ ) 1 2 ( cos ( ( l 3 + 1 2 ) θ 1 4 π ) + o ( 1 ) ) , j 1 , j 2 , j 3 l 3 1 ,