Lecture 16 Generating function, Recurrence Relations for Bessel Function by Dr. Amit Mahajan
What is the Generating function for the Bessel function? What is the integral form of Bessel function? What are recurrence relations for the Bessel functions?
All these questions are answered in this video.
Also the Jacobi series for Bessel function is discussed.
The relation between Bessel function of order -n and n when n is integer is also proved.
This is the 16th video of the Lecture Series in Ordinary Differential Equations and the 9th to talk about the higher order differential equations and 4th on the series solution of ODE.
This lecture requires knowledge of differential calculus of intermediate level. It is presumed that the learner has a basic understanding of mathematical concepts of the intermediate level.
Also do watch the previous lectures for the basics required to understand this lecture.
Lecture 1 : Definition and Formulation of ODE • Lecture 1 Definition & Formulation of an O...
Lecture 2 : First Order and First Degree ODE (separation of variables) • Lecture 2 First Order First Degree ODE's (...
Lecture 3 : First order and First degree ODE (Homogeneous differential equation) • Lecture 3 First Order & First Degree Homog...
Lecture 4 : First Order and First Degree ODE (Leibnitz's Linear Equation) • Lecture 4 First Order Leibnitz's Linear Or...
Lecture 5 : First Order and First Degree Exact Differential Equations • Lecture 5 Exact Differential Equations of ...
Lecture 6 : First Order and Higher Degree Ordinary Differential Equations • Lecture 6 First Order and Higher Degree Or...
Lecture 7 : Orthogonal and Isogonal Trajectories • Lecture 7 Orthogonal & Isogonal Trajectori...
Lecture 8 : Higher Order Linear Differential Equations • Lecture 8 Higher Order Linear Ordinary Dif...
Lecture 9 : Higher Order Linear Non-homogeneous Differential Equations • Lecture 9 Non Homogeneous Ordinary Differe...
Lecture 10 : Cauchy-Euler Differential Equations and Legendre Differential Equations • Lecture 10 Cauchy-Euler and Legendre Diffe...
Lecture 11 : Method of Variation of Parameters and Method of Undetermined Coefficients • Lecture 11 Method of Variation of Paramete...
Lecture 12 : System of simultaneous linear differential equations • Lecture 12 Simultaneous Linear Ordinary Di...
Lecture 13 : Series solution of an ODE about an Ordinary point • Lecture 13 Series solution of ODE about an...
Lecture 14 : Series solution of ODE about a Singular Point • Lecture 14 Series solution of ODE about a ...
Lecture 15 : Series solution of Bessel's Differential Equation • Lecture 15 Series Solution for Bessel's Eq...
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