Geodesic
On Buschman--Erdelyi and Mehler--Fock transforms related to the group $SO_0(3,1)$
Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 228-236

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By using a functional defined on a pair of the assorted represention spaces of the connected subgroup of the proper Lorentz group, a formula for the Buschman–Erdelyi transform of the Legendre function (up to a factor) is derived. Also a formula for the Mehler–Fock transform of the Legendre function of an inverse argument is obtained. Moreover, a generalization of one known formula for the Mehler–Fock transform is derived.
Keywords: Buschman–Erdelyi transform, Mehler–Fock transform, Legendre function. 
@article{CHEB_2023_24_1_a16,
     author = {I. A. Shilin},
     title = {On {Buschman--Erdelyi} and {Mehler--Fock} transforms related to the group $SO_0(3,1)$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {228--236},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a16/}
}
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I. A. Shilin. On Buschman--Erdelyi and Mehler--Fock transforms related to the group $SO_0(3,1)$. Čebyševskij sbornik, Tome 24 (2023) no. 1, pp. 228-236. http://geodesic.mathdoc.fr/item/CHEB_2023_24_1_a16/