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1: Bibliography C
  • J. Chen (1966) On the representation of a large even integer as the sum of a prime and the product of at most two primes. Kexue Tongbao (Foreign Lang. Ed.) 17, pp. 385–386.
  • C. Chiccoli, S. Lorenzutta, and G. Maino (1990b) On a Tricomi series representation for the generalized exponential integral. Internat. J. Comput. Math. 31, pp. 257–262.
  • J. A. Cochran (1966a) The analyticity of cross-product Bessel function zeros. Proc. Cambridge Philos. Soc. 62, pp. 215–226.
  • M. W. Coffey (2008) On some series representations of the Hurwitz zeta function. J. Comput. Appl. Math. 216 (1), pp. 297–305.
  • H. S. Cohl and R. S. Costas-Santos (2020) Multi-Integral Representations for Associated Legendre and Ferrers Functions. Symmetry 12 (10).
  • 2: Bibliography V
  • N. Ja. Vilenkin and A. U. Klimyk (1993) Representation of Lie Groups and Special Functions. Volume 2: Class I Representations, Special Functions, and Integral Transforms. Mathematics and its Applications (Soviet Series), Vol. 74, Kluwer Academic Publishers Group, Dordrecht.
  • N. Ja. Vilenkin (1968) Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.
  • H. Volkmer (1999) Expansions in products of Heine-Stieltjes polynomials. Constr. Approx. 15 (4), pp. 467–480.
  • H. Volkmer (1984) Integral representations for products of Lamé functions by use of fundamental solutions. SIAM J. Math. Anal. 15 (3), pp. 559–569.
  • H. Volkmer (2021) Fourier series representation of Ferrers function 𝖯 .
  • 3: Bibliography S
  • B. E. Sagan (2001) The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. 2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.
  • B. I. Schneider, X. Guan, and K. Bartschat (2016) Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation. Adv. Quantum Chem. 72, pp. 95–127.
  • R. Shail (1980) On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.
  • A. Sharples (1967) Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
  • N. T. Shawagfeh (1992) The Laplace transforms of products of Airy functions. Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.
  • 4: Bibliography R
  • M. Rahman (1981) A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.
  • W. H. Reid (1995) Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.
  • W. H. Reid (1997a) Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.
  • W. H. Reid (1997b) Integral representations for products of Airy functions. III. Quartic products. Z. Angew. Math. Phys. 48 (4), pp. 656–664.
  • M. D. Rogers (2005) Partial fractions expansions and identities for products of Bessel functions. J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
  • 5: Bibliography G
  • A. Gil, J. Segura, and N. M. Temme (2004c) Integral representations for computing real parabolic cylinder functions. Numer. Math. 98 (1), pp. 105–134.
  • A. Gil, J. Segura, and N. M. Temme (2014) Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
  • H. W. Gould (1960) Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
  • K. I. Gross and R. A. Kunze (1976) Bessel functions and representation theory. I. J. Functional Analysis 22 (2), pp. 73–105.
  • E. Grosswald (1985) Representations of Integers as Sums of Squares. Springer-Verlag, New York.
  • 6: 26.9 Integer Partitions: Restricted Number and Part Size
    Table 26.9.1: Partitions p k ( n ) .
    n k
    8 0 1 5 10 15 18 20 21 22 22 22
    A useful representation for a partition is the Ferrers graph in which the integers in the partition are each represented by a row of dots. …
    26.9.4 [ m n ] q = j = 1 n 1 q m n + j 1 q j , n 0 ,
    26.9.5 n = 0 p k ( n ) q n = j = 1 k 1 1 q j = 1 + m = 1 [ k + m 1 m ] q q m ,
    7: 26.13 Permutations: Cycle Notation
    An explicit representation of σ can be given by the 2 × n matrix: … Every permutation is a product of transpositions. … Every transposition is the product of adjacent transpositions. If j < k , then ( j , k ) is a product of 2 k 2 j 1 adjacent transpositions: …Every permutation is a product of adjacent transpositions. …
    8: Bibliography K
  • R. B. Kearfott, M. Dawande, K. Du, and C. Hu (1994) Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.
  • M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
  • A. I. Kheyfits (2004) Closed-form representations of the Lambert W function. Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.
  • A. V. Kitaev and A. H. Vartanian (2004) Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.
  • T. H. Koornwinder (1974) Jacobi polynomials. II. An analytic proof of the product formula. SIAM J. Math. Anal. 5, pp. 125–137.
  • 9: Bibliography B
  • G. Backenstoss (1970) Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.
  • W. N. Bailey (1928) Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
  • Á. Baricz and T. K. Pogány (2013) Integral representations and summations of the modified Struve function. Acta Math. Hungar. 141 (3), pp. 254–281.
  • K. L. Bell and N. S. Scott (1980) Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.
  • W. G. Bickley (1935) Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.
  • 10: Bibliography M
  • O. I. Marichev (1984) On the Representation of Meijer’s G -Function in the Vicinity of Singular Unity. In Complex Analysis and Applications ’81 (Varna, 1981), pp. 383–398.
  • P. Maroni (1995) An integral representation for the Bessel form. J. Comput. Appl. Math. 57 (1-2), pp. 251–260.
  • I. Mező (2020) An integral representation for the Lambert W function.
  • G. F. Miller (1966) On the convergence of the Chebyshev series for functions possessing a singularity in the range of representation. SIAM J. Numer. Anal. 3 (3), pp. 390–409.
  • D. S. Moak (1981) The q -analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.