TLDR:
TLDR:
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What is an integrable systems?
What is an integrable systems?
Integrable systems are dynamical models that have `sufficiently many´ conserved quantities, commonly referred to as conservation laws. These include the conservation of energy and conservation of momenta in many cases, but there are even more conservation laws which are not namned.
Why is it called an integrable system?
Why is it called an integrable system?
The first examples of integrable systems were differential equations that could be solved by integrating them. For example, the Kepler problem is one such example.
What makes Special Functions so special?
What makes Special Functions so special?
They are very useful since special functions come in many different shapes and forms. Not only are special functions solutions to equations that often appear in mathematics and physics, but they are often used as a basis for calculating other functions.
What are elliptic functions?
What are elliptic functions?
Elliptic functions are (complex) mathematical functions that generalize the trigonometric sine and cosine functions. Originally, they were used to calculate the elliptical orbits of planets. Hence the name.
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