Spherical Harmonics in p Dimensions by Christopher Frye, Costas J. Efthimiou
Spherical Harmonics in p Dimensions
Spherical Harmonics in p Dimensions by Christopher Frye, Costas J. Efthimiou
Publisher: arXiv 2012
Number of pages: 95
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before beginning the main subject matter.
Mathematics Analysis & Calculus Harmonic Analysis
Publisher: arXiv 2012
Number of pages: 95
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before beginning the main subject matter.
Mathematics Analysis & Calculus Harmonic Analysis
More Free E-Books For Harmonic Analysis
Similar Books For Harmonic Analysis
1. Introduction to the Theory of Fourier's Series and Integrals by H. S. Carslaw
2. Contributions to Fourier Analysis by A. Zygmund, et al.
3. Spherical Harmonics in p Dimensions by Christopher Frye, Costas J. Efthimiou
4. Lectures on Harmonic Analysis by Thomas Wolff
5. Harmonic Analysis by S.R.S. Varadhan
6. Harmonic Analysis by Russell Brown
7. Nonlinear Fourier Analysis by Terence Tao, Christoph Thiele
8. Lectures on Topics in Mean Periodic Functions and the Two-Radius Theorem by J. Delsarte
9. Lectures on Potential Theory by M. Brelot
10. Lectures on Mean Periodic Functions by J.P. Kahane
11. Notes on Harmonic Analysis by George Benthien
12. An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics by William Elwood Byerly
13. Fourier Series and Systems of Differential Equations and Eigenvalue Problems by Leif Mejlbro
14. Harmonic Function Theory by Sheldon Axler, Paul Bourdon, Wade Ramey
15. Che by shev and Fourier Spectral Methods
16. Linear Partial Differential Equations and Fourier Theory by Marcus Pivato
2. Contributions to Fourier Analysis by A. Zygmund, et al.
3. Spherical Harmonics in p Dimensions by Christopher Frye, Costas J. Efthimiou
4. Lectures on Harmonic Analysis by Thomas Wolff
5. Harmonic Analysis by S.R.S. Varadhan
6. Harmonic Analysis by Russell Brown
7. Nonlinear Fourier Analysis by Terence Tao, Christoph Thiele
8. Lectures on Topics in Mean Periodic Functions and the Two-Radius Theorem by J. Delsarte
9. Lectures on Potential Theory by M. Brelot
10. Lectures on Mean Periodic Functions by J.P. Kahane
11. Notes on Harmonic Analysis by George Benthien
12. An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics by William Elwood Byerly
13. Fourier Series and Systems of Differential Equations and Eigenvalue Problems by Leif Mejlbro
14. Harmonic Function Theory by Sheldon Axler, Paul Bourdon, Wade Ramey
15. Che by shev and Fourier Spectral Methods
16. Linear Partial Differential Equations and Fourier Theory by Marcus Pivato
Categories
- 1. .NET
- 2. Abraham Merritt
- 3. Abstract Algebra
- 4. Academic Writing
- 5. Accelerator Physics
- 6. Accounting
- 7. Acoustics & Sound
- 8. Action & Adventure
- 9. Ada
- 10. Addiction
- 11. Administration
- 12. Administration & Policy
- 13. Advertising
- 14. Aeronautics & Astronautics
- 15. Aerospace
- 16. Africa
- 17. Agile Software Development
- 18. Agricultural Sciences
- 19. AIDS
- 20. AIDS & HIV
- 21. Alexandre Dumas
- 22. Algebra
- 23. Algebraic
- 24. Algebraic Geometry
- 25. Algorithms
- 26. Algorithms & Data Structures
- 27. Allergies
- 28. Amateur
- 29. Analysis & Calculus
- 30. Analytic
- 31. Analytic Geometry
- 32. Analytical
- 33. Anarchism
- 34. Anatole France
- 35. Anatomy
- 36. Ancient
- 37. Android
- 38. AngularJs
- 39. Anna Katharine Green
- 40. Anthony Hope
- 41. Anthony Trollope
- 42. Anthropology
- 43. Anxiety Disorder
- 44. Apocalyptic
- 45. Applications
- 46. Applied
- 47. Applied Mechanics
- 48. Archaeology
- 49. Architecture
- 50. Arthur Conan Doyle
- 51. Arthur Gask
- 52. Arthur Machen
- 53. Arthur Schopenhauer
- 54. Artificial Intelligence
- 55. Arts & Photography
- 56. Asia
- 57. ASP.NET
- 58. Assembly
- 59. Asthma
- 60. Astrobiology
- 61. Astronomy
- 62. Astrophysics
- 63. Atmospheric Sciences
- 64. Atomic Physics
- 65. Atomic, Molecular, & Optical Physics
- 66. Audiobooks
- 67. Audiology & Speech Pathology
- 68. Australia
- 69. Autism
- 70. Automata Theory
- 71. Aviation
- 72. Azure
- 73. Banks & Banking
- 74. Beginning
- 75. Beginning & Introductory
- 76. Benjamin Disraeli
- 77. Biochemistry
- 78. Bioengineering
- 79. Biographies & Memoirs
- 80. Bioinformatics
- 81. Biology
- 82. Blogging & Blogs
- 83. Botany
- 84. Bram Stoker
- 85. Britain
- 86. BSD
- 87. Buddhism
- 88. Business & Culture
- 89. Business & Investing
- 90. C
- 91. C#
- 92. C++
- 93. Calculus
- 94. Calculus of Variations
- 95. Cancer
- 96. Cardiology
- 97. Careers
- 98. Caribbean
- 99. Category Theory
- 100. Celestial Mechanics
- 101. Cell Biology
- 102. Certification Central
- 103. Charles Dickens
- 104. Chemical
- 105. Chemistry
- 106. Chess
- 107. Children's Books
- 108. China
- 109. Christianity
- 110. Church History
- 111. Civil Engineering
- 112. Civil Rights
- 113. Classics
- 114. Clojure
- 115. CoffeeScript
- 116. Combinatorial
- 117. Combinatorics
- 118. Comics & Graphic Novels
- 119. Communication
- 120. Communications
- 121. Commutative Algebra
- 122. Comparative Religion
- 123. Compiler Construction
- 124. Complex Analysis
- 125. Complex Differential Geometry
- 126. Computability Theory
- 127. Computational
- 128. Computational Complexity Theory
- 129. Computer Mathematics
- 130. Computer Science
- 131. Computer Vision
- 132. Computers & Internet
- 133. Concurrent, Parallel & Distributed Systems
- 134. Condensed Matter Physics
- 135. Consciousness & Thought
- 136. Contemporary
- 137. Control Systems
- 138. Cooking, Food & Wine
- 139. Cosmology
- 140. Crime & Criminals
- 141. Cryptography
- 142. Crystallography
- 143. Culinary Arts & Techniques
- 144. Culture
- 145. Cyberpunk
- 146. D. H. Lawrence
- 147. Daniel Defoe
- 148. Databases
- 149. Databases & Information Retrieval
- 150. Debian
- 151. Deep Learning
- 152. Delphi, Pascal
- 153. Design & Architecture
- 154. Design & Decorative Arts
- 155. Diabetes
- 156. Diets & Weight Loss
- 157. Differential
- 158. Differential Equations
- 159. Differential Geometry
- 160. Digital Law
- 161. Digital Music
- 162. Discrete Mathematics
- 163. Diseases
- 164. Disorders & Diseases
- 165. Distance Learning
- 166. Drama
- 167. Drawing
- 168. Dreams
- 169. Dynamical Systems Theory
- 170. Dynamics
- 171. E-Commerce
- 172. E. M. Forster
- 173. E. Phillips Oppenheim
- 174. Earth Sciences
- 175. Eastern
- 176. Ecology
- 177. Econometrics
- 178. Economic Policy & Development
- 179. Economics
- 180. Edgar Allan Poe
- 181. Edgar Rice Burroughs
- 182. Edgar Wallace
- 183. Edith Wharton
- 184. Education
- 185. Educational Psychology
- 186. Edward Bulwer-Lytton
- 187. Egypt
- 188. Electrical Engineering
- 189. Electromagnetics
- 190. Electromagnetism
- 191. Electronic Structure Theory
- 192. Electronics
- 193. Elementary
- 194. Elementary Algebra & Trigonometry
- 195. Elizabeth Gaskell
- 196. Embedded
- 197. Emergency Medicine
- 198. Emigration & Immigration
- 199. Emile Zola
- 200. Endocrinology & Metabolism
- 201. Engineering
- 202. English as a Foreign Language
- 203. Enterprise Edition
- 204. Entertainment
- 205. Entomology
- 206. Environmental Engineering
- 207. Environmental Science
- 208. Epidemiology
- 209. Erlang
- 210. Essays & Travelogues
- 211. Ethics & Morality
- 212. Euclidean Geometry
- 213. Europe
- 214. Evolutionary Algorithms
- 215. Evolutionary Biology
- 216. Exercise & Fitness
- 217. Expeditions & Discoveries
- 218. Experimental Physics
- 219. Extragalactic
- 220. F. Scott Fitzgerald
- 221. Fairy Tales
- 222. Fantasy
- 223. Fashion
- 224. Fedora & Red Hat
- 225. Fergus Hume
- 226. Field Theory
- 227. Fields & Galois Theory
- 228. Finance
- 229. Financial Management
- 230. Flash
- 231. Fluid Mechanics
- 232. Fluid Mechanics & Hydraulics
- 233. Foreign Languages
- 234. Forth
- 235. Fortran
- 236. France
- 237. Functional Analysis
- 238. Functional Programming
- 239. Fyodor Dostoyevsky
- 240. G. A. Henty
- 241. G. K. Chesterton
- 242. Galactic
- 243. Game Programming
- 244. Game Theory
- 245. Gastroenterology
- 246. General
- 247. General & Introductory
- 248. General Relativity
- 249. Genetics
- 250. Genre Fiction
- 251. Geographic Information Systems
- 252. Geography
- 253. Geology
- 254. Geometric
- 255. Geometry & Physics
- 256. Geometry & Topology
- 257. Geophysics
- 258. George Eliot
- 259. George Gissing
- 260. George Orwell
- 261. Git
- 262. Go Programming
- 263. Graph Theory
- 264. Graphic Design
- 265. Graphics & Games
- 266. Graphics & Multimedia
- 267. Graphics Programming
- 268. Graphics, Sound & Games
- 269. Group Theory
- 270. Guy Boothby
- 271. H. G. Wells
- 272. H. P. Lovecraft
- 273. Handheld & Mobile Devices
- 274. Hard SF
- 275. Hardware
- 276. Harmonic Analysis
- 277. Harold MacGrath
- 278. Haskell
- 279. Health, Mind & Body
- 280. Heart Disease
- 281. Hematology
- 282. Henry James
- 283. Henry Rider Haggard
- 284. Hepatitis
- 285. Hiking & Camping
- 286. Hinduism
- 287. Historical
- 288. History
- 289. History & Criticism
- 290. History & Surveys
- 291. Home Computing
- 292. Honore de Balzac
- 293. Horror
- 294. Human Resource Management
- 295. Human Rights
- 296. Humanities
- 297. Humor
- 298. Hunting & Fishing
- 299. IBM DB2
- 300. Image Processing
- 301. Immunology
- 302. India
- 303. Industrial Engineering
- 304. Industries & Professions
- 305. Infectious Disease
- 306. Inflation
- 307. Information & Coding Theory
- 308. Information Retrieval
- 309. Information Science
- 310. Information Technology in Education
- 311. Inorganic
- 312. Instrumentation
- 313. Intellectual Property
- 314. Internal Medicine
- 315. International
- 316. International Business
- 317. International Law
- 318. Internet
- 319. Intranets & Extranets
- 320. Introductory
- 321. Introductory Guides
- 322. Investing
- 323. iPad/iPhone/iOS
- 324. Islam
- 325. IT Management
- 326. J. Sheridan Le Fanu
- 327. Jack London
- 328. James Joyce
- 329. Jane Austen
- 330. Japan
- 331. Japanese
- 332. Java
- 333. Java Tools & Utilities
- 334. JavaScript
- 335. Job Hunting & Careers
- 336. Job Interviews
- 337. John Blaine
- 338. John Buchan
- 339. John Galsworthy
- 340. Jon Evans
- 341. Joseph Conrad
- 342. Josephine Tey
- 343. Journalism
- 344. Judaism
- 345. Jules Verne
- 346. K-theory
- 347. Knut Hamsun
- 348. L. Frank Baum
- 349. Lagrangian
- 350. Languages & Tools
- 351. Law
- 352. Leaders & Politicians
- 353. Leadership
- 354. Lie Groups
- 355. Linear Algebra
- 356. Linguistics
- 357. Linux
- 358. Linux for Beginners
- 359. Lisp
- 360. Literary
- 361. Literature
- 362. Literature & Fiction
- 363. Logic
- 364. Louis Tracy
- 365. M. P. Shiel
- 366. Machine Learning
- 367. Macroeconomics
- 368. Management & Leadership
- 369. Marine Engineering
- 370. Mark Twain
- 371. Marketing & Sales
- 372. Materials Science
- 373. Math Games
- 374. Mathematical & Statistical
- 375. Mathematical Methods
- 376. Mathematical Physics
- 377. Mathematics
- 378. MATLAB
- 379. Matrices
- 380. Mechanical Engineering
- 381. Mechanics
- 382. Mechatronics & Robotics
- 383. Media Studies
- 384. Medicine
- 385. Mental Health
- 386. Microbiology
- 387. Microcontrollers
- 388. Microeconomics
- 389. Microelectronics
- 390. Microprocessors & System Design
- 391. Microsoft
- 392. Middle East
- 393. Military
- 394. Military Science
- 395. Military SF
- 396. Mobile App Development
- 397. Modal Logic
- 398. Model Theory
- 399. Modeling & Simulation
- 400. Molecular Biology
- 401. Money & Monetary Policy
- 402. MongoDB
- 403. Motion & Manipulation
- 404. Mountaineering
- 405. Movie
- 406. Multivariable
- 407. Music
- 408. Mystery & Detective
- 409. Mysticism
- 410. Mythology
- 411. Nanostructures
- 412. Nanotechnology
- 413. Nathaniel Hawthorne
- 414. Natural Language Processing
- 415. Network Security
- 416. Networking
- 417. Networks, Protocols & APIs
- 418. Neural Networks
- 419. Neurology
- 420. Neuroscience
- 421. Non-Euclidean Geometries
- 422. Noncommutative Geometry
- 423. Nonfiction
- 424. Nonlinear Optics
- 425. Nonprofit Organizations & Charities
- 426. North America
- 427. Nuclear Physics
- 428. Number Theory
- 429. Numerical Analysis
- 430. Nutrition
- 431. Object-Oriented Programming
- 432. Objective Caml (OCaml)
- 433. Objective-C
- 434. Observational
- 435. Obstetrics & Gynecology
- 436. Oceanography
- 437. Oncology
- 438. Open Source
- 439. Operating Systems
- 440. Operations & Project Management
- 441. Ophthalmology
- 442. Optics
- 443. Optimal Control
- 444. Optimization
- 445. Oracle
- 446. Order, Lattices, Representation Theory
- 447. Ordinary
- 448. Organic
- 449. Ornithology
- 450. Oscar Wilde
- 451. Oscillations & Waves
- 452. Other Eastern Religions
- 453. Outdoors & Nature
- 454. Painting
- 455. Partial
- 456. Particle Physics
- 457. Path Integral Formulation
- 458. PCs
- 459. Pediatrics
- 460. Perl & CGI
- 461. Personal Finance
- 462. Personal Health
- 463. Pharmacology
- 464. Philosophy
- 465. Photography
- 466. PHP
- 467. Physical Chemistry
- 468. Physician & Patient
- 469. Physics
- 470. Physiology
- 471. Planetary science
- 472. Plasma Physics
- 473. Poetry
- 474. Point-set
- 475. Political Science
- 476. Politics
- 477. Popular
- 478. Popular & Elementary
- 479. PostgreSQL
- 480. Power Engineering
- 481. PowerPoint
- 482. Preventive Medicine
- 483. Privacy
- 484. Probability
- 485. Probability & Statistics
- 486. Programming
- 487. Programming Language Theory
- 488. Prolog
- 489. Proof Theory
- 490. Propulsion Technology
- 491. Protestantism
- 492. Psychiatry
- 493. Psychoanalysis
- 494. Psychology
- 495. Psychology & Counseling
- 496. Public Health
- 497. Public Relations
- 498. Pulmonary
- 499. Pure Mathematics
- 500. Puzzles & Games
- 501. Python
- 502. Quantum Chromodynamics
- 503. Quantum Computing
- 504. Quantum Field Theory
- 505. Quantum Gravity
- 506. Quantum Mechanics
- 507. Quantum Optics
- 508. Quaternions
- 509. R Programming Language
- 510. Radiology
- 511. Rafael Sabatini
- 512. Real Analysis
- 513. Recipes
- 514. Recording & Sound
- 515. Recovery
- 516. Reference
- 517. Relationships
- 518. Relativity & Gravitation
- 519. Religion & Spirituality
- 520. Religious
- 521. Religious Studies
- 522. Renewable Energy
- 523. Richard Marsh
- 524. Riemannian Geometry
- 525. Robert Louis Stevenson
- 526. Robert Michael Ballantyne
- 527. Robotics & Automation
- 528. Robust Control
- 529. Romance
- 530. Rome
- 531. Ruby
- 532. Rudyard Kipling
- 533. Safety & First Aid
- 534. Sales & Selling
- 535. Scala
- 536. Scheme
- 537. Science
- 538. Science & Technology
- 539. Science Fiction
- 540. Science Fiction & Fantasy
- 541. Scientific
- 542. Sculpture
- 543. Security & Cryptography
- 544. Self-Help
- 545. Self-Improvement
- 546. Set Theory
- 547. Sex
- 548. Short Stories
- 549. Signal Processing
- 550. Sinclair Lewis
- 551. Single Variable
- 552. Small Business & Entrepreneurship
- 553. Smalltalk
- 554. Social Aspects
- 555. Social Media
- 556. Social Sciences
- 557. Sociology
- 558. Soft & Social SF
- 559. Software
- 560. Software Design, Testing & Engineering
- 561. Software Engineering
- 562. Software Project Management
- 563. Solar
- 564. Solid State Physics
- 565. South America
- 566. Space Opera
- 567. Spanish
- 568. Special Relativity
- 569. Spectroscopy
- 570. Speech Processing
- 571. Spreadsheets
- 572. SQL
- 573. SQL Server
- 574. Statistical Physics
- 575. Statistics
- 576. Stellar
- 577. Stochastic Calculus
- 578. Stocks
- 579. Strategic Management & Organizational Studies
- 580. Strategy
- 581. Strength of Materials & Solid Mechanics
- 582. String Theory
- 583. Study & Teaching
- 584. Substance Abuse
- 585. Superconductivity
- 586. Supergravity
- 587. Superhuman
- 588. Supersymmetry
- 589. Surgery
- 590. Symplectic & Contact Geometry
- 591. Systems Theory
- 592. Tcl/Tk
- 593. Technology
- 594. Technology & Society
- 595. Telecommunications
- 596. Telephone Systems
- 597. Templates & Libraries
- 598. Tensor Calculus
- 599. Terrorism
- 600. TeX/LaTeX
- 601. Theodore Dreiser
- 602. Theology
- 603. Theory of Computation
- 604. Theory, Composition & Performance
- 605. Thermodynamics
- 606. Thermodynamics, Heat Transfer & Energy Conversion
- 607. Thomas Hardy
- 608. Thrillers
- 609. Time Travel & Alternate History
- 610. Topology
- 611. Transportation Engineering
- 612. Travel
- 613. Trigonometry
- 614. Tuberculosis
- 615. Twitter
- 616. Type Theory
- 617. Ubuntu
- 618. United States
- 619. Unix
- 620. User Interface Design
- 621. Vector Analysis
- 622. Version Control
- 623. VHDL
- 624. Victor Hugo
- 625. Video Games
- 626. Virginia Woolf
- 627. Visual Basic
- 628. Walter Scott
- 629. Wavelets
- 630. Web Design
- 631. Web Development
- 632. Web Marketing
- 633. Web Programming
- 634. Web Services
- 635. Westerns
- 636. Wilkie Collins
- 637. Willa Cather
- 638. William Hope Hodgson
- 639. William Makepeace Thackeray
- 640. William Morris
- 641. Windows 7
- 642. Windows Phone
- 643. Wireless Networks
- 644. Word Processing
- 645. WordPress
- 646. Working Abroad
- 647. World
- 648. World Literature
- 649. Writers
- 650. Writing Skills
- 651. XML
- 652. Zane Grey
- 653. Zoology