Math. Physics (III)
- Gamma functions (factorial function), Euler's definite integral, Euler-Gauss formula, Weierstrass formula
- Euler's reflection formula, Complex integral representation of gamma function, Digamma and Polygamma functions, Beta function
- Solving Bessel's differential equation using the Frobenius method, Bessel functions of the first kind, Generating function
- Recurrence relations, Integral representation for the Bessel functions of the first kind, Complex integral representation of the Bessel functions of the first kind
- Orthogonality of the Bessel functions of the first kind, Bessel-Fourier series, Bessel functions of the second kind, Neumann function, Recurrence relations
- Hankel functions, Spherical Bessel functions and the recurrence relations
- Modified Bessel's differential equation, Modified Bessel functions of the first kind, Series form, Recurrene relations
- Modified Bessel functions of the second kind and the recurrene relations, Legendre differential equation, Solving Legendre differential equation using the Frobenius method
- Series form of the Legendre polinomials (Legendre functions of the first kind), Rodrigues' formula, Generating function and the recurrence relations, Orthogonality of Legendre polynomials
- Legendre series, Generalized Legendre differential equation, Associated Legendre functions and their orthogonality relation
- Spherical harmonics, Legendre functions of the second kind, Hermite differential equation, Hermite polynomials
- Generating function for Hermite polynomials and the recurrence relations, Orthogonality of Hermite polynomials, Rodrigues' formula, Laguerre differential equation, Laguerre polynomials
- Generation function for Laguerre polynomials and the recurrence relations, Rodrigues' formula, Associated Laguerre functions and the recurrence relations
- Green's functions for boundary value problems
- Solving ordinary differential equations by using Green's functions
- Properties of Green's functions