Generalized fractional integration of Bessel function of the first kind. (English) Zbl 1156.26004
The authors study two integral transforms involving the \({}_2F_1\) hypergeometric function. These integral transforms are generalizations of both Riemann-Liouville fractional integrals and Erdélyi-Kober fractional integrals. The integral transforms are applied to the Bessel function of the first kind of order \(\nu\). The special cases \(\nu=-1/2\) and \(\nu=1/2\) finally lead to fractional integrals involving the cosine and the sine function, respectively.
Reviewer: Roelof Koekoek (Delft)
MSC:
26A33 | Fractional derivatives and integrals |
33C05 | Classical hypergeometric functions, \({}_2F_1\) |
33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
33C20 | Generalized hypergeometric series, \({}_pF_q\) |
33C60 | Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) |
26A09 | Elementary functions |
Keywords:
fractional integral transforms; Bessel function of the first kind; hypergeometric function; generalized hypergeometric functionReferences:
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