Topic
Legendre function
About: Legendre function is a research topic. Over the lifetime, 1826 publications have been published within this topic receiving 58783 citations.
Papers published on a yearly basis
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Papers
Book•
1 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
28,896 citations
Book•
1 Jun 1961
TL;DR: In this paper, a revised version of the Revised edition of the book has been published, with a new introduction to the concept of plane wave functions and spherical wave functions, as well as a detailed discussion of the properties of these functions.
Abstract: Foreword to the Revised Edition. Preface. Fundamental Concepts. Introduction to Waves. Some Theorems and Concepts. Plane Wave Functions. Cylindrical Wave Functions. Spherical Wave Functions. Perturbational and Variational Techniques. Microwave Networks. Appendix A: Vector Analysis. Appendix B: Complex Permittivities. Appendix C: Fourier Series and Integrals. Appendix D: Bessel Functions. Appendix E: Legendre Functions. Bibliography. Index.
6,270 citations
Book•
1 Jan 1997
TL;DR: In this article, a central force gravity field model is used for inertial navigation with assistance from external measurements. But this model is not suitable for the Kalman Filter State Variable Error Models.
Abstract: Part 1 Inertial Navigation: Notation, Coordinate Systems and Units Equations of Motion in a Central Force Gravity Field Inertial Instrumentation Calibration Initial Alignment and Attitude Computation Geodetic Variables and Constants Equations of Motion with General Gravity Model. Part 2 Inertial Navigation with Aids: Inertial Navigation with External Measurements Error Equations for the Kalman Filter State Variable Error Models. Part 3 Accuracy Analysis: Accuracy Criteria and Analysis Techniques Error Equations for Calibration, Alignment and Initialization Evaluation of Gravity Model Error Effects. Appendices: Matrix Inverse Formulas LaPlace Transforms Quaternions Associated Legendre Functions Associated Legendre Function Derivatives Procedure for Generating Gravity Disturbance Realizations Procedure for Generating Specific Force Profile.
546 citations
Book•
1 Jan 1986TL;DR: The representation of acoustic and electromagnetic fields the special theory of relativity radiation resonators the theory of waveguides refraction surface waves scattering by smooth objects diffraction by edges transient waves.
Abstract: The representation of acoustic and electromagnetic fields the special theory of relativity radiation resonators the theory of waveguides refraction surface waves scattering by smooth objects diffraction by edges transient waves. Appendices: Bessel functions Legendre functions Mathieu functions parabolic cylinder functions spheroidal functions tensor calculus asymptotic evaluation of integrals.
518 citations
TL;DR: In this article, the authors derived translation theorems for spherical vector wave functions in a reduced form by the use of formulas relating the coefficients that arise in expansion of the product of two associated Legendre functions.
Abstract: : Translational addition theorems for spherical vector wave functions are derived in a reduced form. The reduction is accomplished by the use of formulas relating the coefficients that arise in expansion of the product of two associated Legendre functions. These addition theorems should be useful in those cases in which spherical vector wave functions are used where the distances of bodies and sources are separated by the order of a few wavelengths.
462 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 9 |
| 2024 | 29 |
| 2023 | 42 |
| 2022 | 94 |
| 2021 | 23 |
| 2020 | 28 |