Schwarz%20lemma

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1: 1.10 Functions of a Complex Variable

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Schwarz Reflection Principle

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Schwarz’s Lemma

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2: 1.7 Inequalities

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Cauchy–Schwarz Inequality

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Cauchy–Schwarz Inequality

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3: Bibliography G

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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software 20 (1), pp. 21–62.

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Notes:

For remark see same journal 24(1998), p. 355.

External Links:

Document, ISSN 0098-3500, GAMS (module 726; package TOMS), ZentralBlatt

Referenced by:

2nd item, §3.5(v), §3.5(v).

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

Encodings:

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Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.

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External Links:

ISSN 0003-4916, Link, MathReview (A. O. Barut), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

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Superstring Theory: Introduction, Vol. 1. 2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-35752-7, MathReview, ZentralBlatt

Referenced by:

§20.12(ii), 3rd item.

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Superstring Theory: Loop Amplitudes, Anomalies and Phenomenolgy, Vol. 2. 2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-35753-5, MathReview, ZentralBlatt

Referenced by:

§20.12(ii).

Encodings:

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4: 20 Theta Functions

Chapter 20 Theta Functions

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5: Bibliography

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Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

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External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

Encodings:

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On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.

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External Links:

ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

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Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

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External Links:

ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

Encodings:

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A trinomial analogue of Bailey’s lemma and $N=2$ superconformal invariance. Comm. Math. Phys. 192 (2), pp. 245–260.

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External Links:

ISSN 0010-3616, Document, MathReview (Anne Schilling), ZentralBlatt

Referenced by:

§17.12.

Encodings:

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Bailey’s Transform, Lemma, Chains and Tree. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.

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External Links:

ISBN 0-7923-7119-4, MathReview, ZentralBlatt

Referenced by:

§17.12.

Encodings:

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6: 17.12 Bailey Pairs

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Weak Bailey Lemma

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Strong Bailey Lemma

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7: 8 Incomplete Gamma and Related
Functions

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8: 28 Mathieu Functions and Hill’s Equation

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9: 11.6 Asymptotic Expansions

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$c_3(\lambda )=20{\lambda }^{-6}-4{\lambda }^{-4},$

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10: Bibliography W

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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External Links:

ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

Encodings:

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A note on the trinomial analogue of Bailey’s lemma. J. Combin. Theory Ser. A 81 (1), pp. 114–118.

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External Links:

ISSN 0097-3165, Document, MathReview (Anne Schilling), ZentralBlatt

Referenced by:

§17.12.

Encodings:

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