GENERALIZED HYPERGEOMETRIC FUNCTIONS AND FRACTIONAL CALCULUS
Paper Code:
MAT143 B
Credits:
4
Contact Hours:
60.00
Max. Marks:
100.00
Unit I:
I
Generalized Hypergeometric function-Definition, Convergence of the series for , Differential equation and its solution, Contiguous function relations, Saalschutz’s theorem, whipple’s theorem. Contour integral representation for , Eulerian type integrals involving , Integral representation for .
Unit II:
II
Meijer’s G function- Definition, Elementary properties, Multiplication formulas, Derivatives, Mellin and Laplace transforms of the G- function.
Unit III:
III
H-function of one variable: Definition, Identities, Special cases, Differentiation formulas, Recurrence and contiguous function relations, Finite and infinite series, Fourier series for the H-function, Simple finite and infinite integrals involving the H-function.
Unit IV:
IV
Fractional Calculus: Definition and elementary properties of Riemann-Liouville fractional integral and derivatives, Derivative of the fractional integral, The fractional integral of derivatives.
Unit V:
V
Leibnitz’s formula for fractional integral and fractional derivatives, Law of exponent, Image of elementary and generalized hypergeometric function under fractional integrals and derivatives.
Essential Readings:
- W.N. Bailey, Generalized Hyper Geometric Series, Cambridge tracts in Mathematical and Mathematical Physics No. 32, Cambridge University Press, 1935.
- A.M. Mathai, R.K. Saxena, Generalized Hyper Geometric Functions with Applications in Statistic and Physical Sciences, Springer- Verlag, Lecture Notes Series No. 348, Heidelberg and New York, 1973.
- A.M. Mathai, R.K.Saxena,The H-Function with Applications in Statistic and Other Disciplines, John Wiley and sons, New York,1978.
- E. D. Rainville, Special Functions, Macmillan, New York,1960.
- I.N. Sneddon, Special Functions of Mathematical Physics and Chemistry, 2nd edition, Oliver and Boyd Edinburgh, 1961..
- Kenneth Miller, Bertram Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley-Interscience, 1 edition, 1993.
- Rudolf Hilfer, Applications of Fractional Calculus in Physics, World Scientific, 2000.
Academic Year:
