Geodesic
A survey of Buschman~--- Erdelyi transmutations
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 4, pp. 63-93

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This is a survey paper. In introduction some historical and priority information is given. The author's convenient classification of Buschman — Erdelyi transmutations is proposed. Based on this classification results on Buschman — Erdelyi transmutations of the first, second and third kinds are surveyed, including unitarian Sonine — Katrakhov and Poisson — Katrakhov transmutations. In the last section applications of Buschman — Erdelyi transmutations are considered.
Keywords: transmutation, integral transform, Buschman — Erdelyi transmutation, Erdelyi — Kober operator, Sonine — Poisson operator, fractional integral. 
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     author = {S. M. Sitnik},
     title = {A survey of {Buschman~---} {Erdelyi} transmutations},
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     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_4_a4/}
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S. M. Sitnik. A survey of Buschman~--- Erdelyi transmutations. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 4, pp. 63-93. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_4_a4/