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Elliptic functions: a primer /
Elliptic Functions: A Primer defines and describes what is an elliptic function, attempts to have a more elementary approach to them, and drastically reduce the complications of its classic formulae; from which the book proceeds to a more detailed study of the subject while being reasonably complete...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1971]
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| Edición: | First edition]. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Elliptic Functions: A Primer; Copyright Page ; Table of Contents; EDITOR'S PREFACE; LIST OF TABLES; Chapter 1. Double periodicity; Equivalent bases; Chapter 2. Lattices; Chapter 3. Multiples and sub-multiples of periods; Chapter 4. Fundamental parallelogram; Liouville's theorem-a doubly periodic function without accessible singularities is a constant; Chapter 5. Definition of an elliptic function; A rational function of an elliptic function is an elliptic function; Chapter 6. An elliptic function (unless constant) has poles and zeros Identification of an elliptic function.
- (I) by poles and principal parts(ii) by poles and zeros; Chapter 7. Residue sum of an elliptic function is zero; Chapter 8. Derivative of an elliptic function; Order of an elliptic function; No functions of the first order; Chapter 9. Additive pseudoperiodicity; Integration of an elliptic function with zero residues; Signature; Evaluation of A�
- B(\ for a function additively pseudoperiodic in �a, �a with moduli A, �A; Chapter 10. Pole-sum of an elliptic function; Chapter 11. The mid-lattice points; Odd and even elliptic functions; Chapter 12. Construction of the function ...
- Chapter 13. Construction and periodicity of the Weierstrassian function ... Chapter 14. Zeros of..z; The constants ef, eg, eh; Construction of the primitive functions fj z, gj z, hj z; Chapter 15. Periodicity of the primitive functions; Primitive functions are odd functions with simple poles; Structure patterns and residue patterns; Double series for fj z; Chapter 16. Construction and pseudoperiodicity of ... ; The constants nf, ng, nh; Laurent series for ... ; Chapter 17. Construction of �oz ...
- Chapter 18. Construction, in terms of ... and ... of an elliptic function with assigned poles and principal partsExpression for ... ; Constant value of ... ; Chapter 19. Construction, in terms of �o�, of an elliptic function with assigned poles and zeros; Expression for ... ; Expression for the primitive function pjz; Chapter 20. Expression of an elliptic function in the form ... ; Chapter 21. Expression for.'2z in terms of.z; Evaluation of ... ; Chapter 22. Expression of an elliptic function in the form S ... ; Chapter 23. Elliptic functions on the same lattice are connected algebraically.
- Chapter 24. The six critical constants pqf2g + g2g + h2f =0; fgfh = gfhf; gr = vfg; Chapter 25. Quarter-period addition to the argument of a primitive function; The twelve elementary functions; pq z qp z = qp'wq; pqz qrz = pqwr, prz; Periods and poles of pq z; Relations between the squares of the elementary functions; Chapter 26. The functions pz and pqz as solutions of differential equations; Chapter 27. Copolar functions and simultaneous differential equations; Chapter 28. Addition theorems for pz and .z and .z; ... + fj'z/fjz; Chapter 29. Addition theorems for fjz, jfz and hgz.