Pandit S.N. Shukla University, Shahdol (M.P) M.Sc. MATHEMATICS SEMESTER-IV Paper II-Advanced Special Function-II Syllabus

Ashok Nayak
0

Pandit S.N. Shukla University, Shahdol (M.P) M.Sc. MATHEMATICS SEMESTER-IV Paper II-Advanced Special Function-II Syllabus

Theory Paper : Max. Marks- 42 

Internal Assessment: Max. Marks- 08

Note: The question paper will consist of three sections A, B&C. Section A will consist of objeclive type questions each carrving 1 marks, section B will consist of 5 short answer type questions cach earrying 3 marks and section C will consist of 2 long answer type questions each carrying 10 marks. Section B & C will have internal choice. 


Unit 1- Bessel Function and Legendre polynomials: Definition of J(Z). Bessel's differential equation, Generating function, Bessel's integral with index half and an odd integer. 

Unit 2- Generating function for Legendre polynomials, Rodrigues formula, Bateman's generating function, Additional generating functions. Hypergeometric forms of P.(X). 


Unit 3- Special properties of Pa(X). Some more generating functions, Laplace's first integral form, Orthogonality. 

Unit 4- Definition of Hermite polynomials H-(X). Pure recurrence relations, Differential recurrence relations, Rodrigue's formula, Other generating functions, Orthogonality, Expansion of polynomials, more generating functions. 


Unit 5- The Laguerre Polynomials L-(X). Generating functions, Pure recurrence relations, Differential recurrence relation, Rodrigue's formula, Orthogonality, Expansion of polynomials, special properties, Other generating functions. 


Recommended Books: 

[1]E.D. Rainville, Special Functions, The Macmillan Co., New York, 1971. 

[2] H.M.Srivastava, K.C.Gupta and S.P.Goyal, The H-function of One and Two variables with applications, South Asian Publication, New Delhi, 

[3] N . Saran, S.D.Sharma and Trivedi, Special Functions with applications, Pragati Prakashan, 1986. 

[4] N.N.Lebdev, Special functions and their applications, Prentice Hall, Englewood Cliffs, New Jersey, USA, 1965.

Post a Comment

0 Comments
* Please Don't Spam Here. All the Comments are Reviewed by Admin.
Post a Comment (0)
Our website uses cookies to enhance your experience. Learn More
Accept !

Adblocker detected! Please consider reading this notice.

We've detected that you are using AdBlock Plus or some other adblocking software which is preventing the page from fully loading.

We don't have any banner, Flash, animation, obnoxious sound, or popup ad. We do not implement these annoying types of ads!

We need money to operate the site, and almost all of it comes from our online advertising.

×