Applications of Basic Hypergeometric Functions

C. R. Adams, Linear q-difference equations, Bull. Amer. Math. Soc., 37 (1931), 361–400

R. P. Agarwal, Arun Verma, Generalized basic hypergeometric series with unconnected bases, Proc. Cambridge Philos. Soc., 63 (1967), 727–734

R. P. Agarwal, Arun Verma, Generalized basic hypergeometric series with unconnected bases. II, Quart. J. Math. Oxford Ser. (2), 18 (1967), 181–192

H. L. Alder, Partition identities—from Euler to the present, Amer. Math. Monthly, 76 (1969), 733–746

George E. Andrews, On q-difference equations for certain well-poised basic hypergeometric series, Quart. J. Math. Oxford Ser. (2), 19 (1968), 433–447

George E. Andrews, On a transformation of bilateral series with applications, Proc. Amer. Math. Soc., 25 (1970), 554–558

George E. Andrews, On a partition problem of J. J. Sylvester, J. London Math. Soc. (2), 2 (1970), 571–576

George E. Andrews, On the foundations of combinatorial theory. V. Eulerian differential operators, Studies in Appl. Math., 50 (1971), 345–375

George E. Andrews, Partition identities, Advances in Math., 9 (1972), 10–51

George E. Andrews, Number theory, W. B. Saunders Co., Philadelphia, Pa., 1971x+259

George E. Andrews, On the q-analog of Kummer's theorem and applications, Duke Math. J., 40 (1973), 525–528

G. E. Andrews, On a computer program for summing series of binomial coefficients, in preparation

A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14–32

W. N. Bailey, Series of hypergeometric type which are infinite in both directions, Quart. J. Math., 7 (1936), 105–115

W. N. Bailey, Generalized hypergeometric series, Cambridge Mathematical Tract No. 32, Cambridge University Press, Cambridge, 1935

W. N. Bailey, A note on certain q-identities, Quart. J. Math., Oxford Ser., 12 (1941), 173–175

W. N. Bailey, A note on two of Ramanujan's formulae, Quart. J. Math., Oxford Ser. (2), 3 (1952), 29–31

W. N. Bailey, On the simplification of some identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (3), 1 (1951), 217–221

W. N. Bailey, On the basic bilateral hypergeometric series $\sb 2\Psi\sb 2$, Quart. J. Math., Oxford Ser. (2), 1 (1950), 194–198

M. Baker, D. Coon, Dual resonance theory with nonlinear trajectories, Phys. Rev. D, 2 (1970), 2349–2358

Edward A. Bender, A generalized q-binomial Vandermonde convolution, Discrete Math., 1 (1971/1972), 115–119

O. Bottema, Die Schwingungen eines zusammengesetzten Pendels, Jber. Deutsche Math.-Verein., 42 (1932), 42–60

L. Carlitz, On a problem of the history of Chinese mathematics, Mat. Lapok, 6 (1955), 219–220

L. Carlitz, Some polynomials related to theta functions, Ann. Mat. Pura Appl. (4), 41 (1956), 359–373

L. Carlitz, M. V. Subbarao, A simple proof of the quintuple product identity, Proc. Amer. Math. Soc., 32 (1972), 42–44

P. Cartier, D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Mathematics, No. 85, Springer-Verlag, Berlin, 1969iv+88

A. Cayley, Note on a Partition-Series, Amer. J. Math., 6 (1883/84), 63–64

T. W. Chaundy, F. H. Jackson, J. London Math. Soc., 37 (1962), 126–128, (obituary)

J. A. Daum, The basic analogue of Kummer's theorem, Bull. Amer. Math. Soc., 48 (1942), 711–713

Harold T. Davis, The summation of series, The Principia Press of Trinity University, San Antonio, Tex., 1962ix+140

H. Göllnitz, Partitionen mit Differenzenbedingungen, J. Reine Angew. Math., 225 (1967), 154–190

B. Gordon, Some identities in combinatorial analysis, Quart. J. Math. Oxford Ser. (2), 12 (1961), 285–290

H. W. Gould, A new symmetrical combinatorial identity, J. Combinatorial Theory Ser. A, 13 (1972), 278–286

H. W. Gould, The case of the strange binomial identities of Professor Moriarty, Fibonacci Quart., 10 (1962), 381–391, 402

Henry W. Gould, Combinatorial identities, Henry W. Gould, Morgantown, W.Va., 1972viii+106

Wolfgang Hahn, Beiträge zur Theorie der Heineschen Reihen. Die $24$ Integrale der Hypergeometrischen q-Differenzengleichung. Das q-Analogon der Laplace-Transformation, Math. Nachr., 2 (1949), 340–379

Wolfgang Hahn, Über die höheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen, Math. Nachr., 3 (1950), 257–294

Wolfgang Hahn, Die mechanische Deutung einer geometrischen Differenzgleichung, Z. Angew. Math. Mech., 33 (1953), 270–272

G. H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, Oxford, 1960

E. Heine, Handbuch die Kugelfunctionen; Theorie and Anwendung, Vol. I, Reimer, Berlin, 1878

Michael Henle, Binomial enumeration on dissects, Trans. Amer. Math. Soc., 202 (1975), 1–39

Donald E. Knuth, Subspaces, subsets, and partitions, J. Combinatorial Theory Ser. A, 10 (1971), 178–180

T. M. MacRobert, Functions of a Complex Variable, Macmillan, London, 1958

L. J. Mordell, On the representation of numbers as the sum of $2r$ squares, Quart. J. Math., 48 (1920), 93–104

V. Ramamani, K. Venkatachaliengar, On a partition theorem of Sylvester, Michigan Math. J., 19 (1972), 137–140

John Riordan, Combinatorial identities, John Wiley & Sons Inc., New York, 1968xiii+256

Jay Goldman, Gian-Carlo Rota, W. T. Tutte, The number of subspaces of a vector spaceRecent Progress in Combinatorics (Proc. Third Waterloo Conf. on Combinatorics, 1968), Academic Press, New York, 1969, 75–83

Jay Goldman, Gian-Carlo Rota, On the foundations of combinatorial theory. IV. Finite vector spaces and Eulerian generating functions, Studies in Appl. Math., 49 (1970), 239–258

Ronald Mullin, Gian-Carlo Rota, B. Harris, On the foundations of combinatorial theory. III. Theory of binomial enumerationGraph Theory and its Applications (Proc. Advanced Sem., Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1969), Academic Press, New York, 1970, 167–213 (loose errata)

W. W. Sawyer, Prelude to mathematics, Penguin Books, 1955, 214–, Baltimore

L. J. Slater, A. Lakin, Two proofs of the $\sb 6\Psi\sb 6$ summation theorem, Proc. Edinburgh Math. Soc. (2), 9 (1956), 116–121

Lucy Joan Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966xiii+273

J. J. Sylvester, F. Franklin, A Constructive Theory of Partitions, Arranged in Three Acts, an Interact and an Exodion, Amer. J. Math., 5 (1882), 251–330, 6 (1884), pp. 334–336; (or Collected Mathematical Papers of James Joseph Sylvester, vol. 4, Cambridge University Press, Cambridge, 1912, pp. 1–83)

N. G. van Kampen, Exact calculation of the fluctuation spectrum for a nonlinear model system, J. Mathematical Phys., 2 (1961), 592–601