# Pandit S.N. Shukla University, Shahdol (M.P) M.Sc. MATHEMATICS SEMESTER-IV Paper III -Jacobi Polynomials and H- Function II Syllabus

## Pandit S.N. Shukla University, Shahdol (M.P) M.Sc. MATHEMATICS SEMESTER-IV Paper III -Jacobi Polynomials and H- 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 7  dejective type questions cach cary ing I marks, section B will consist of 5 short answer ty pe questions each carrying 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- Differentiation formulas of H-function of one variable, Partial derivatives with respect to parameters. Contiguous relation and simple expansion formula.

Unit 2- The H-function of two variables, Definition and notation. Asymptotic behavior, elementary properties, Special cases.

Unit 3- Derivatives, Contiguous relations, Total count of recurrences, Definite integrals of H- function of one variable.

Unit 4- Finite summation formula for the Il-function of two variables Double & Triple integrals of H-function of one variable.

Unit 5- Method and scheme for obtaining sum of finite or infinite series. Double summation formulas.

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.

Reference Books:

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

[2] E.T. Whittaker and G.N. Watson, A Course of Modern Analysis, Cambridge University Press, London, 1963.