Unit I
Gamma and Beta Functions and Elliptic Functions
Part II: 4.1 – 4.11
| Course Name | Special Functions |
| Course Code | 25MAT335 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | Electives: Mathematics |
| Campus | Mysuru |
Gamma and Beta Functions and Elliptic Functions
Part II: 4.1 – 4.11
Special functions , power series solution of differential equations, ordinary point ; Solution about singular points , Frobenius method. Bessel’s equation, solution of Bessel’s equation, Bessel’s functions Jn(x).
Part II: 8.5-8.6, 8.8- 8.10, 11.1, 11.2.
Legendre’s equation, Legendre’s polynomial Pn(x), Legendre’s function of the second kind [Qn(x)], General solution of Legendre’s equation, Rodrigue’s formula, Legendre polynomials, A generating function of Legendre’s polynomial.
Part II: 9.1-9.4.
Orthogonality of Legendre polynomials, Recurrence formulae for Pn(x) Green’s function – Green’s Identities – Generalized functions
Part II: 9.8-9.9, 9.22-9.25.
Objectives: To enable students to
• Understand gamma and beta functions
• Solve the Legendre equations using various techniques
Text books:
1. M.D. Raisinghania , Ordinary and Partial Differential Equations, S.Chand, 18th edition, 2016
References:
1. I. N. Sneddon – Special Functions of mathematical Physics & Chemistry, 3 Oliver & Boyd, Lon-don.
2. N. N. Lebedev – Special Functions and Their Applications , PHI.
3. Special Functions, R. Askey and R. Roy, Cambridge.
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