Ramanujan’s

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11: Bibliography B

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Ramanujan’s theories of elliptic functions to alternative bases. Trans. Amer. Math. Soc. 347 (11), pp. 4163–4244.

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External Links:

ISSN 0002-9947, FullText, MathReview (J. Borwein), ZentralBlatt

Referenced by:

§15.8(v), §20.11(iii).

Encodings:

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Chapter 13 of Ramanujan’s second notebook: Integrals and asymptotic expansions. Expo. Math. 2 (4), pp. 289–347.

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External Links:

ISSN 0723-0869, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.10(iii).

Encodings:

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Ramanujan’s Notebooks. Part II. Springer-Verlag, New York.

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External Links:

ISBN 0-387-96794-X, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§15.7.

Encodings:

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Ramanujan’s Notebooks. Part III. Springer-Verlag, Berlin-New York.

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External Links:

ISBN 0-387-97503-9, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§17.13.

Encodings:

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12: 19.9 Inequalities

… ►Ramanujan’s approximation and its leading error term yield the following approximation to $L(a,b)/(\pi (a+b))$: …Barnard et al. (2000) shows that nine of the thirteen approximations, including Ramanujan’s, are from below and four are from above. …

13: Bibliography L

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Ramanujan’s function $\tau (n)$ . Duke Math. J. 10 (3), pp. 483–492.

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External Links:

Document, MathReview (H. S. Zuckerman), ZentralBlatt

Referenced by:

§27.20, §27.20, §27.21.

Encodings:

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The vanishing of Ramanujan’s function $\tau (n)$ . Duke Math. J. 14 (2), pp. 429–433.

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External Links:

Document, MathReview (R. A. Rankin), ZentralBlatt

Referenced by:

§27.14(vi).

Encodings:

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14: Bibliography W

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A table of Ramanujan’s function $\tau (n)$ . Proc. London Math. Soc. (2) 51, pp. 1–13.

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External Links:

Document, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§27.21.

Encodings:

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15: Bibliography

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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).

Encodings:

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16: 15.8 Transformations of Variable

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Ramanujan’s Cubic Transformation

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17: Bibliography D

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Ramanujan’s master theorem for symmetric cones. Pacific J. Math. 175 (2), pp. 447–490.

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External Links:

ISSN 0030-8730, MathReview (Jacques Faraut), ZentralBlatt

Referenced by:

§35.7(ii), §35.8(iv), §35.8(v).

Encodings:

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18: Bibliography H

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Asymptotic formulae in combinatory analysis. Proc. London Math. Soc. (2) 17, pp. 75–115.

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Notes:

Reprinted in Ramanujan (1962, pp. 276–309).

External Links:

Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(iii).

Encodings:

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19: Bibliography M

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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.

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External Links:

Document, ZentralBlatt

Referenced by:

§27.13(iv).

Encodings:

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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.

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External Links:

ISSN 0027-8424, MathReview (Ken Ono), ZentralBlatt

Referenced by:

§27.13(iv).

Encodings:

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20: Bibliography C

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On Ramanujan’s cubic transformation formula for ${}_2{}^{}F_1^{}(\frac{1}{3},\frac{2}{3};1;z)$ . Math. Proc. Cambridge Philos. Soc. 124 (2), pp. 193–204.

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External Links:

ISSN 0305-0041, Document, MathReview (Aleksander Grytczuk), ZentralBlatt

Referenced by:

§15.8(v).

Encodings:

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