The contiguous function relations for the basic hypergeometric series
نویسندگان
چکیده
منابع مشابه
Contiguous relations of hypergeometric series
The 15 Gauss contiguous relations for 2F1 hypergeometric series imply that any three 2F1 series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We prove several properties of coefficients of these general contiguous relations, and use the results to propose effective ways to compute contiguous relations. We also di...
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ess as: 2), http: athemat s.2012.0 Abstract Two Gauss functions are said to be contiguous if they are alike except for one pair of parameters, and these differ by unity. Contiguous relations are of great use in extending numerical tables of the function. In this paper we will introduce a new method for computing such types of relations. a 2012 Egyptian Mathematical Society. Production and hosti...
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The second order hypergeometric q-difference operator is studied for the value c = −q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l(Z). The operator has deficiency indices (1, 1) and we describe as explicitly as possible the spectral resolutions of the self-adjoint extensions. This gives rise to one-parameter o...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1990
ISSN: 0022-247X
DOI: 10.1016/0022-247x(90)90292-n