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  • Produktbild: Theory of Incomplete Cylindrical Functions and their Applications
  • Produktbild: Theory of Incomplete Cylindrical Functions and their Applications
Band 160

Theory of Incomplete Cylindrical Functions and their Applications

Aus der Reihe Grundlehren der mathematischen Wissenschaften

49,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

11.11.2011

Verlag

Springer Berlin

Seitenzahl

332

Maße (L/B/H)

22,9/15,2/1,9 cm

Gewicht

504 g

Auflage

Softcover reprint of the original 1st ed. 1971

Übersetzt von

Henry Eason Fettis + weitere

Sprache

Englisch

ISBN

978-3-642-65023-9

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

11.11.2011

Verlag

Springer Berlin

Seitenzahl

332

Maße (L/B/H)

22,9/15,2/1,9 cm

Gewicht

504 g

Auflage

Softcover reprint of the original 1st ed. 1971

Übersetzt von

  • Henry Eason Fettis
  • J.W. Goresh
  • D.A. Lee

Sprache

Englisch

ISBN

978-3-642-65023-9

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Theory of Incomplete Cylindrical Functions and their Applications
  • Produktbild: Theory of Incomplete Cylindrical Functions and their Applications
  • I. Some Information from the Theory of Cylindrical Functions.- 1. The Differential Equation and Recursion Relationships for Cylindrical Functions.- 2. Generalized System of Functional Equations for Cylindrical Functions and the Inhomogenious Bessel Differential Equation.- 3. Integral Repesentations of Cylindrical Functions in the Poisson Form.- 4. Integral Representations of Cylindrical Functions of the Bessel-Schlaefli and Sonine Form.- II. General Theory of Incomplete Cylindrical Functions Expressed in Poisson Form.- 1. Definitions of Incomplete Cylindrical Functions as Poisson Integrals.- 2. Recurrence Relations for the Incomplete Cylindrical Functions.- 3. Some General Properties of Incomplete Cylindrical Functions.- 4. Differential Equations for Incomplete Cylindrical Functions.- 5. Incomplete Lipschitz-Hankel Integrals.- 6. The Relation between the Incomplete Lipschitz-Hankel Integrals and Incomplete Cylindrical Functions of Poisson Form.- 7. Series Representations for Incomplete Cylindrical Functions.- 8. Incomplete Beta and Gamma Functions and their Relation to Hypergeometric Functions.- 9. Asymptotic Series and Methods for their Construction.- 10. Asymptotic Expansion for Incomplete Cylindrical Functions of Poisson Form.- III. Incomplete Cylindrical Functions of Bessel Form.- 1. Definitions of Incomplete Cylindrical Functions of Bessel Form.- 2. Recursion Relations and Differential Equations for the Function ?v (w, z).- 3. Connection between Incomplete Cylindrical Functions of the Poisson and Bessel Forms.- 4. Incomplete Cylindrical Functions of Bessel Form with Half-Odd Indices.- 5. A Generating Function, Addition Formula, and Series for the Function ?v (w, z).- 6. Asymptotic Expansions for Incomplete Cylindrical Functions of the Bessel Form.- 7. Asymptotic Expansions for Incomplete Cylindrical Functions; the General Case.- 8. Incomplete Airy Integrals and their Generalizations.- 9. Asymptotic Expansions of Incomplete Cylindrical Functions of the Bessel Form for Large Indices.- IV. Incomplete Cylindrical Functions of Sonine-Schlaefli Form and the Incomplete Weber Integrals.- 1. The Concept of Incomplete Cylindrical Functions of Whittaker Form.- 2. Incomplete Cylindrical Functions of Sonine-Schlaefli Form and their Basic Properties.- 3. Incomplete Weber Integrals.- 4. The Connection between the Incomplete Weber Integral, Incomplete Cylindrical Functions, and Lipschitz-Hankel Integrals.- 5. The Connection between Incomplete Integrals of Weber, Lipschitz-Hankel and Incomplete Cylindrical Functions of Poisson Form.- 6. The Connection between Incomplete Weber Integrals and Lommel Functions of Two Variables.- V. Incomplete Cylindrical Functions of Real Arguments and their Relation to Certain Discontinuous Integrals.- 1. Incomplete Cylindrical Functions of Real Arguments.- 2. Unit Functions and their Basic Characteristics.- 3. New Integral Representations for Incomplete Cylindrical Functions of Real Arguments.- 4. Relation between Weber Integrals of Bessel Functions and Incomplete Cylindrical Functions.- 5. Discontinuous Integrals of Gallop and their Relation to Incomplete Cylindrical Functions.- 6. Sonine’s Discontinuous Integral and its Connection with Incomplete Bessel Functions.- VI. Integrals Involving Incomplete Cylindrical Functions.- 1. Improper Integral of Lipschitz-Hankel.- 2. Integrals of Weber Type Involving Incomplete Cylindrical Functions.- 3. Improper Integrals of Certain Incomplete Cylindrical Functions with Respect to Index.- 4. Some Discontinuous Integrals of Weher-Schafheitlin Type Involving Incomplete Cylindrical Functions.- 5. Improper Integrals of Hankel Type Involving Incomplete Cylindrical Functions.- 6. Definite Integrals Containing Incomplete Cylindrical Functions.- VII. Application of Incomplete Cylindrical Functions to Problems of Wave Propagation and Diffraction.- 1. Connections between Incomplete Cylindrical Functions and some Tabulated Special Integrals.- 2. Absorption of Radiation in the Earth’s Atmosphere.- 3. Radiation from a Vertical Dipole on the Earth’s Surface.- 4. The Problem of Diffraction by a Wedge.- 5. Diffraction of Waves by a Screen of Given Form.- 6. Some Problems in the Theory of Diffraction in Optical Apparatus.- VIII. Application of Incomplete Cylindrical Functions to some Problems of Solid State Theory and the Motion of Charged Particles in Electromagnetic Fields.- 1. Computation of Radiation and Absorption Fields in the Theory of Multiphonon Processes.- 2. Scattering of Light by Atoms with Interference of Excited States.- 3. Motion of Charged Particles in Constant Electric and Time-Varying Magnetic Fields.- 4. Motion of Charged Particles in Changing Electric and Magnetic Fields.- IX. Applications of Incomplete Cylindrical Functions to some Problems of Atomic and Nuclear Physics.- 1. Solution of a Particular Form of the Schrödinger Equation.- 2. Some Relations for Evaluating the Transparency Coefficients of Nuclei and the Average Loss of Impulse for Interaction of Particles with their Fields.- 3. Resonant Absorption of Radiation in Media of Finite Dimensions.- 4. Application of Incomplete Cylindrical Functions in the Study of a Heterogeneous Reactor with Small Number of Blocks.- 5. Application of Incomplete Cylindrical Functions to the Solution of the Diffusion Equation.- X. Other Applied Problems Leading to Incomplete Cylindrical Functions.- 1. Excitation of Betatron Oscillations.- 2. Transient Processes in Electrical and Microphonic Circuits.- 3. Influence of Optical Systems on the Amplitude of Transmitted Waves.- 4. Density Perturbation in a Gas due to a Rapidly Moving Body.- 5. Computation of the Sound Field in Closed Domains.- 6. Exchange Processes between Liquid and Solid Phases.- 7. Drift of Non-Fundamental Carriers in Semiconductors.- 8. Damping of Radiation in High Temperature Plasma in the Presence of Shielding.- 9. Other Special Integrals.- XI. Compendium of Tables and Computation Formulae for Evaluation of Incomplete Cylindrical Functions.- 1. Incomplete Bessel Functions, Struve Functions, Anger Functions, and Weber Functions.- 2. Incomplete Hankel Functions and MacDonald Functions.- 3. Incomplete Lipschitz-Hankel Integrals.- 4. Incomplete Weber Integrals.- 5. Tables of Incomplete Cylindrical Functions.- Author Index.