The present book embodies the researches carried out at the Aligarh Muslim University, Aligarh. The Bessel Functions originally introduced by Bessel in 1824, while discussing a problem in astronomy. The Bessel Functions received the most extensive treatment among all the Special Functions. W. Voigt (1850-1919) introduced the functions K(x,y) and L(x,y) which play an important role in several diverse fields of physics. Later Srivastava and Miller (1987) established a link between Bessel Functions and generalized Voigt functions. The Voigt functions were subsequently modified by others e.g. Exton, Srivastava and Chen, Klusch, Siddiqui, Srivastava, Pathan, etc.