Higher Derivatives of Airy Functions and of their Products
Copyright policy )Higher Derivatives of Airy Functions and of their Products
The problem of evaluation of higher derivatives of Airy functions in a closed form is investigated. General expressions for the polynomials which have arisen in explicit formulae for these derivatives are given in terms of particular values of Gegenbauer polynomials. Similar problem for products of Airy functions is solved in terms of terminating hypergeometric series.
Generalized hypergeometric series, \({}_pF_q\), FOS: Physical sciences, hypergeometric function, Mathematical Physics (math-ph), 33C10, 33C05, 33C20, Gegenbauer polynomials, Classical hypergeometric functions, \({}_2F_1\), Airy functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Mathematical Physics
Generalized hypergeometric series, \({}_pF_q\), FOS: Physical sciences, hypergeometric function, Mathematical Physics (math-ph), 33C10, 33C05, 33C20, Gegenbauer polynomials, Classical hypergeometric functions, \({}_2F_1\), Airy functions, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Mathematical Physics
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