Weierstrass Factorization Theorem and Its Applications (ongoing)
A transcendental function which has infinite numbers of zero can be written in a form of infinite products of linear polynomials.
Mathematical Physics
Hypergeometric Differential Equation
An useful ordinary differenctial equation
Generating Function and Integral Representation of the Bessel Function
The Bessel function can be expressed not only in an infinite series form, but also in an integral form.
The Method of Steepest Descent and Asymptotic Forms of Airy Function
The most powerful tool when obtaining an asymptotic approximation of a real-valued function