Ramanujan%20congruences

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1: Bibliography

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Congruences of $p$-adic integer order Bernoulli numbers. J. Number Theory 59 (2), pp. 374–388.

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External Links:

ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.16(iii).

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Chapter $16$ of Ramanujan’s second notebook: Theta-functions and $q$-series. Mem. Amer. Math. Soc. 53 (315), pp. v+85.

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External Links:

ISSN 0065-9266, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§20.11(ii).

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Ramanujan Revisited. Academic Press Inc., Boston, MA.

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External Links:

ISBN 0-12-058560-X, ISBN 0-12-058560-X, MathReview, ZentralBlatt

Referenced by:

§20.11(ii), Profile Richard A. Askey.

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Congruences for the $q$-secant numbers. European J. Combin. 1 (4), pp. 283–287.

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External Links:

ISSN 0195-6698, MathReview (J. E. Cigler), ZentralBlatt

Referenced by:

§24.16(iii).

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Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.

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External Links:

ISSN 0030-8730, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.12.

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2: Bibliography K

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Asymptotic expansions of certain $q$-series and a formula of Ramanujan for specific values of the Riemann zeta function. Acta Arith. 107 (3), pp. 269–298.

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External Links:

ISSN 0065-1036, Document, Link, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§17.2(i).

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The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers. Math. Ann. 216 (1), pp. 1–4.

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ISSN 0025-5831, Document, MathReview (M. Basmakov), ZentralBlatt

Referenced by:

§24.16(iii).

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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

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External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

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The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.

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External Links:

ISSN 1382-4090, Document, FullText, MathReview (José Luis López), ZentralBlatt

Referenced by:

§18.26(v), §18.26(v).

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3: Bibliography R

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Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.

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External Links:

ISSN 0025-5874, ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(v).

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Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,

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Referenced by:

§24.7(i).

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Collected Papers of Srinivasa Ramanujan. Chelsea Publishing Co., New York.

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Notes:

Reprinted with commentary by Bruce Berndt, AMS Chelsea Publishing Series, American Mathematical Society (2000).

External Links:

ISBN 0-8218-2076-1

Referenced by:

§8.11(v), G. H. Hardy and S. Ramanujan (1918).

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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External Links:

ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

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4: Bibliography P

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Orthogonal polynomials and some $q$-beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (2), pp. 517–540.

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External Links:

ISSN 0022-247X, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.33(iv), §18.33(v).

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

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Voronoi type congruences for Bernoulli numbers. In Voronoi’s Impact on Modern Science. Book I, P. Engel and H. Syta (Eds.),

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External Links:

ZentralBlatt

Referenced by:

§24.10(iii).

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