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1: Bibliography H
  • P. I. Hadži (1973) The Laplace transform for expressions that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).
  • P. I. Hadži (1975a) Certain integrals that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1975 (2), pp. 8688, 95 (Russian).
  • P. I. Hadži (1975b) Integrals containing the Fresnel functions S ( x ) and C ( x ) . Bul. Akad. Štiince RSS Moldoven. 1975 (3), pp. 48–60, 93 (Russian).
  • P. I. Hadži (1978) Sums with cylindrical functions that reduce to the probability function and to related functions. Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).
  • F. E. Harris (2002) Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion. Internat. J. Quantum Chem. 88 (6), pp. 701–734.
  • 2: Bibliography
  • D. E. Amos, S. L. Daniel, and M. K. Weston (1977) Algorithm 511: CDC 6600 subroutines IBESS and JBESS for Bessel functions I ν ( x ) and J ν ( x ) , x 0 , ν 0 . ACM Trans. Math. Software 3 (1), pp. 9395.
  • W. L. Anderson (1982) Algorithm 588. Fast Hankel transforms using related and lagged convolutions. ACM Trans. Math. Software 8 (4), pp. 369–370.
  • G. E. Andrews, R. Askey, and R. Roy (1999) Special Functions. Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge.
  • G. E. Andrews and D. Foata (1980) Congruences for the q -secant numbers. European J. Combin. 1 (4), pp. 283–287.
  • B. H. Armstrong (1967) Spectrum line profiles: The Voigt function. J. Quant. Spectrosc. Radiat. Transfer 7, pp. 61–88.
  • 3: 3.9 Acceleration of Convergence
    For further information on the epsilon algorithm see Brezinski and Redivo Zaglia (1991, pp. 78–95). …
    Table 3.9.1: Shanks’ transformation for s n = j = 1 n ( 1 ) j + 1 j 2 .
    n t n , 2 t n , 4 t n , 6 t n , 8 t n , 10
    4 0.82221 76684 88 0.82246 28314 41 0.82246 69467 93 0.82246 70314 36 0.82246 70333 75
    8 0.82243 73137 33 0.82246 67719 32 0.82246 70301 49 0.82246 70333 73 0.82246 70334 23
    10 0.82245 30535 15 0.82246 69397 57 0.82246 70324 88 0.82246 70334 12 0.82246 70334 24
    4: Bibliography K
  • K. W. J. Kadell (1994) A proof of the q -Macdonald-Morris conjecture for B C n . Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
  • T. A. Kaeding (1995) Pascal program for generating tables of SU ( 3 ) Clebsch-Gordan coefficients. Comput. Phys. Comm. 85 (1), pp. 82–88.
  • E. H. Kaufman and T. D. Lenker (1986) Linear convergence and the bisection algorithm. Amer. Math. Monthly 93 (1), pp. 48–51.
  • N. D. Kazarinoff (1988) Special functions and the Bieberbach conjecture. Amer. Math. Monthly 95 (8), pp. 689–696.
  • E. D. Krupnikov and K. S. Kölbig (1997) Some special cases of the generalized hypergeometric function F q q + 1 . J. Comput. Appl. Math. 78 (1), pp. 79–95.
  • 5: Bibliography U
  • F. Ursell (1960) On Kelvin’s ship-wave pattern. J. Fluid Mech. 8 (3), pp. 418–431.
  • F. Ursell (1984) Integrals with a large parameter: Legendre functions of large degree and fixed order. Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.
  • 6: 29.7 Asymptotic Expansions
    29.7.6 τ 2 = 1 2 10 ( 1 + k 2 ) ( 1 k 2 ) 2 ( 5 p 4 + 34 p 2 + 9 ) ,
    29.7.7 τ 3 = p 2 14 ( ( 1 + k 2 ) 4 ( 33 p 4 + 410 p 2 + 405 ) 24 k 2 ( 1 + k 2 ) 2 ( 7 p 4 + 90 p 2 + 95 ) + 16 k 4 ( 9 p 4 + 130 p 2 + 173 ) ) ,
    29.7.8 τ 4 = 1 2 16 ( ( 1 + k 2 ) 5 ( 63 p 6 + 1260 p 4 + 2943 p 2 + 486 ) 8 k 2 ( 1 + k 2 ) 3 ( 49 p 6 + 1010 p 4 + 2493 p 2 + 432 ) + 16 k 4 ( 1 + k 2 ) ( 35 p 6 + 760 p 4 + 2043 p 2 + 378 ) ) .
    7: 33.16 Connection Formulas
    §33.16(i) F and G in Terms of f and h
    where C ( η ) is given by (33.2.5) or (33.2.6).
    §33.16(ii) f and h in Terms of F and G when ϵ > 0
    and again define A ( ϵ , ) by (33.14.11) or (33.14.12). … and again define A ( ϵ , ) by (33.14.11) or (33.14.12). …
    8: Bibliography O
  • A. B. Olde Daalhuis (1998b) Hyperterminants. II. J. Comput. Appl. Math. 89 (1), pp. 87–95.
  • 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 (1977a) Connection formulas for second-order differential equations with multiple turning points. SIAM J. Math. Anal. 8 (1), pp. 127–154.
  • F. W. J. Olver (1995) On an asymptotic expansion of a ratio of gamma functions. Proc. Roy. Irish Acad. Sect. A 95 (1), pp. 5–9.
  • C. Osácar, J. Palacián, and M. Palacios (1995) Numerical evaluation of the dilogarithm of complex argument. Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.
  • 9: Bibliography T
  • J. D. Talman (1983) LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 9399.
  • I. C. Tang (1969) Some definite integrals and Fourier series for Jacobian elliptic functions. Z. Angew. Math. Mech. 49, pp. 95–96.
  • N. M. Temme (1994a) A set of algorithms for the incomplete gamma functions. Probab. Engrg. Inform. Sci. 8, pp. 291–307.
  • N. M. Temme (1995b) Bernoulli polynomials old and new: Generalizations and asymptotics. CWI Quarterly 8 (1), pp. 47–66.
  • J. Todd (1975) The lemniscate constants. Comm. ACM 18 (1), pp. 14–19.
  • 10: Bibliography M
  • L. C. Maximon (1955) On the evaluation of indefinite integrals involving the special functions: Application of method. Quart. Appl. Math. 13, pp. 84–93.
  • Fr. Mechel (1966) Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.
  • S. C. Milne (1996) New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function. Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
  • S. C. Milne (1997) Balanced Θ 2 3 summation theorems for U ( n ) basic hypergeometric series. Adv. Math. 131 (1), pp. 93–187.
  • L. J. Mordell (1917) On the representation of numbers as a sum of 2 r squares. Quarterly Journal of Math. 48, pp. 93–104.