Certain properties for a class of analytic functions associated with hypergeometric functions (original) (raw)
Journal of Numerical Analysis and Approximation Theory
https://doi.org/10.33993/JNAAT432-1023
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Abstract
In this particular paper, we investigate coefficient inequalities, closure theorems, convolution properties for the functions belonging to the class \( \mathcal{S}^{m,r,s}_{\lambda_1,\lambda_2}(\eta)\). Further, integral transforms of functions in the same class are also discussed.
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Throughout the present note we abbreviate the set of p parameters a1,…,ap by (ap), with similar interpretations for (bq), etc. Also, by [(ap)]m we mean the product , where [λ]m = Г(λ + m)/ Г(λ), and so on. One of the main results we give here is the expansion formula(1)which is valid, by analytic continuation, when, p,q,r,s,t and u are nonnegative integers such that p+r < q+s+l (or p+r = q+s+l and |zω| <1), p+t < q+u (or p + t = q + u and |z| < 1), and the various parameters including μ are so restricted that each side of equation (1) has a meaning.
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References (8)
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