A STUDY OF A Q-ANALOGUE OF MACROBERT'S E-FUNCTION.
Item
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Title
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A STUDY OF A Q-ANALOGUE OF MACROBERT'S E-FUNCTION.
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Identifier
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AAI8119682
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identifier
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8119682
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Creator
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KUSH, SATINDRA NATH.
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Contributor
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Harvey Cohn
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Date
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1981
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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(1)Definition of E-function as defined by MacRobert in 1937 to give a meaning to generalized hypergeometric function. (,p)F(,q){lcub}(alpha)(,1),...,(alpha)(,p); (beta)(,1),...,p(,q): z{rcub}. (2)Definition of a q-analogue given by R. P. Agarwal and its integral representation. (3)Properties of E ((alpha),(beta):z) and recurrence relation. (4)Definition of generalized E(,q)-function and its various representations. (5)Recurrence relation involving E(,q)(r,(alpha)(,p): s(beta)(,t):z). (6)Contour integrals of E(,q)(r,(alpha)(,p): s,(beta)(,t):z). (7)Basic analogue of Whittaker functions. (8)Certain expansion of basic generalized MacRoberts E-function. (9)Simple and general expansions. Finfinite expension and expansions with a basic binomial factors. (10)Certain lemmas to prove condition for convergence. (11)Statement of main theorem and its proof involving certain general expansion of basic generalized MacRobert's E-function. (12)Special cases of the main theorem. (13)Condition of convergence under which the main theorem is valid. (14)Integration involving the q-analogue of generalized MacRobert's E-function, with respect to their parameter. (15)Statement of the main theorem and evaluation of the main integral. (16)Certain known cases and evaluation of certain new integrals. (17)Certain summations of bilateral series. (18)Integration of basic E-function with respect to its parameters where the contours are of Slater type. (19)Statement of the main theorem and its evaluation. (20)Special cases.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Mathematics
