Geodesic
On computation of the Bessel function by summing up the series
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 453-472

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Two algorithms for an effective calculation of the Bessel function are presented: a fast algorithm with an increasing accuracy of computation and a computational algorithm for the case of a large argument of the Bessel function. 
@article{SJVM_2019_22_4_a4,
     author = {E. A. Karatsuba},
     title = {On computation of the {Bessel} function by summing up the series},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {453--472},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a4/}
}
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E. A. Karatsuba. On computation of the Bessel function by summing up the series. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 22 (2019) no. 4, pp. 453-472. http://geodesic.mathdoc.fr/item/SJVM_2019_22_4_a4/