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RIEMANN‐LIOUVILLE FRACTIONAL CALCULUS OF CERTAIN FINITE CLASS OF CLASSICAL ORTHOGONAL POLYNOMIALS

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann‐Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.