Welcome to this blog: ELLIPTIC FUNCTIONS

Dear Reader,

   I welcome you to this blog on elliptic functions. It is aimed at mathematically oriented readers, regardless of their formal education in the subject.The only mathematical preparation that is necessary to read the greater part of it is a sound high school education. The relevant material on elementary algebra, trigonometry and calculus can be easily found in downloadable textbooks readily available on the internet. (They are no longer in copyright. Therefore, downloading them is perfectly legal.)

 The few results involving complex functions that need to be known for a perusal of some items can be learnt through self-study, from legally admissible publications available on the internet.

 It is not known to me whether this is the first  and the only blog on the internet devoted entirely to elliptic functions. Perhaps it is. Perhaps it is not.

What are elliptic functions? I give below an informal definition.

 The trigonometric functions sin u and cos u are well known to all who have studied mathematics in high school. It is known that they are periodic functions, having the period pi : sin (u+pi) = sin  u, cos (u+pi)= cos u. They are actually special cases, or rather, limiting cases, of certain functions which are periodic, having two periods. These are called elliptic functions. Hence, the trigonometric functions can be called singly periodic functions, and the elliptic functions doubly periodic.

  A formal definition, more carefully worded than this informal one, can be easily found in reliable sites on the internet.

  Although the theory of trigonometric functions is routinely taught in detail in secondary school and high school, the theory of elliptic functions is usually not taught nowadays at any educational level. At some institutions, special courses on this theory are sometimes taught. But these are rare and are usually elective rather than compulsory. Hence, the natural progression of a student's education from the mathematics of single periodicity to that of double periodicity often does not occur at all. Whereas it is impossible for any person to earn a university degree in mathematics, physics or engineering without knowing at least the fundamentals of the theory of trigonometric functions, it is possible, rather unfortunately, to earn such a degree without knowing anything at all about elliptic functions.

  In this blog, elliptic functions will be freely discussed, with a view to creating a greater awareness of them amongst mathematically oriented people than is at present possible in routine institutional education.

  I thank you for visiting this blog and cordially request you to visit it often.

Yours sincerely,
Somjit Datta, Ph.D