Schwarz reflection principle

SearchAdvancedHelp

(0.001 seconds)

1—10 of 51 matching pages

1: 1.10 Functions of a Complex Variable

… ►

Schwarz Reflection Principle

… ►

Phase (or Argument) Principle

… ►

§1.10(v) Maximum-Modulus Principle

►

Analytic Functions

… ►

Schwarz’s Lemma

…

2: 10.11 Analytic Continuation

…

3: 1.7 Inequalities

… ►

Cauchy–Schwarz Inequality

… ►

Cauchy–Schwarz Inequality

…

4: Bibliography F

… ►

Transverse cusp diffraction catastrophes produced by the reflection of ultrasonic tone bursts from a curved surface in water. J. Acoust. Soc. Amer. 92 (5), pp. 2869–2877.

ⓘ

External Links:

Document

Referenced by:

§36.14(iv).

Encodings:

BibTeX

►

Travel time surface of a transverse cusp caustic produced by reflection of acoustical transients from a curved metal surface. J. Acoust. Soc. Amer. 95 (2), pp. 650–660.

ⓘ

External Links:

Document

Referenced by:

§36.14(iv).

Encodings:

BibTeX

… ►

Principles and Techniques of Applied Mathematics. Dover, New York.

ⓘ

Notes:

Reprint of First Edition, 1956, John-Wiley: New York

External Links:

ISBN 0-486-66444-9, MathReview Entry

Referenced by:

§1.16(ix), §1.17(ii), §1.17(ii), §1.17(i), §1.17(i), §1.17(iv), §1.18(ix), §1.18(iii), §1.18(vi), §1.18(i), §1.18(x).

Encodings:

BibTeX

…

5: 25.4 Reflection Formulas

§25.4 Reflection Formulas

… ►

25.4.1 $$\zeta \left(1-s\right)=2{(2\pi )}^{-s}\cos \left(\frac{1}{2}\pi s\right)\mathrm{\Gamma }\left(s\right)\zeta \left(s\right),$$

ⓘ

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $\zeta \left(s\right)$: Riemann zeta function, $\pi$: the ratio of the circumference of a circle to its diameter, $\cos z$: cosine function and $s$: complex variable

Keywords:

reflection formula

Source:

Apostol (1976, (12), p. 259)

Referenced by:

§25.10(i), §5.17

Permalink:

http://dlmf.nist.gov/25.4.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §25.4 and Ch.25

►

25.4.2 $$\zeta \left(s\right)=2{(2\pi )}^{s-1}\sin \left(\frac{1}{2}\pi s\right)\mathrm{\Gamma }\left(1-s\right)\zeta \left(1-s\right).$$

ⓘ

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $\zeta \left(s\right)$: Riemann zeta function, $\pi$: the ratio of the circumference of a circle to its diameter, $\sin z$: sine function and $s$: complex variable

Keywords:

reflection formula

Source:

Apostol (1976, (13), p. 259)

A&S Ref:

23.2.6

Permalink:

http://dlmf.nist.gov/25.4.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §25.4 and Ch.25

… ►

25.4.3 $$\xi \left(s\right)=\xi \left(1-s\right),$$

ⓘ

Symbols:

$\xi \left(s\right)$: Riemann’s $\xi$-function and $s$: complex variable

Keywords:

reflection formula

Source:

Apostol (1976, p. 260)

Permalink:

http://dlmf.nist.gov/25.4.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §25.4 and Ch.25

…

6: 26.6 Other Lattice Path Numbers

…

7: Bibliography G

… ►

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

ⓘ

External Links:

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

Referenced by:

§20.12(ii), 3rd item.

Encodings:

BibTeX

►

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

ⓘ

External Links:

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

Referenced by:

§20.12(ii).

Encodings:

BibTeX

…

8: 5.21 Methods of Computation

… ►For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3). …

9: Preface

… ►The term digital library has gained acceptance for this kind of information resource, and our choice of project title reflects our hope that the NIST DLMF will be a vehicle for revolutionizing the way applicable mathematics in general is practiced and delivered.

10: 5.5 Functional Relations

… ►

§5.5(ii) Reflection

►

5.5.3 $$\mathrm{\Gamma }\left(z\right)\mathrm{\Gamma }\left(1-z\right)=\pi /\sin \left(\pi z\right),$$ $z\ne 0,\pm 1,\mathrm{\dots }$,

ⓘ

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $\sin z$: sine function and $z$: complex variable

A&S Ref:

6.1.17 (without the condition on $z$.)

Referenced by:

§10.19(i), §15.4(ii), §15.8(ii), (25.9.2), §5.21, (9.10.18), (9.12.15)

Permalink:

http://dlmf.nist.gov/5.5.E3

Encodings:

pMML, png, TeX

See also:

Annotations for §5.5(ii), §5.5 and Ch.5

…