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1999•Methods and Applications of AnalysisOpen access

Addition formulas for $q$-Legendre-type functions

Mizan Rahman, Q. M. Tariq

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Abstract

TWO families of addition formula for g-Legendre-type polynomials are obtained by application of known product formulas of Askey-Wilson and g-Racah polynomials.It is shown that the formula involving the g-Racah polynomials also leads to a ^-analogue of the classical addition formula for the nonterminating Legendre functions.Unlike the quantum group-theoretic methods used by Koelink to obtain essentially the same formulas, our method is purely analytic based on qr-series techniques.

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TWO families of addition formula for g-Legendre-type polynomials are obtained by application of known product formulas of Askey-Wilson and g-Racah polynomials.It is shown that the formula involving the g-Racah polynomials also leads to a ^-analogue of the classical addition formula for the nonterminating Legendre functions.Unlike the quantum group-theoretic methods used by Koelink to obtain essentially the same formulas, our method is purely analytic based on qr-series techniques.

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Available abstract

TWO families of addition formula for g-Legendre-type polynomials are obtained by application of known product formulas of Askey-Wilson and g-Racah polynomials.It is shown that the formula involving the g-Racah polynomials also leads to a ^-analogue of the classical addition formula for the nonterminating Legendre functions.Unlike the quantum group-theoretic methods used by Koelink to obtain essentially the same formulas, our method is purely analytic based on qr-series techniques.

Key concepts: Mathematics, Legendre polynomials, Type (biology), Legendre's equation, Legendre function, Pure mathematics, Algebra over a field, Mathematical analysis

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