Returns to the origin for a randomized random walk
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 25 (1971) no. 3, p. 389-395 
@article{ASNSP_1971_3_25_3_389_0,
     author = {Gibson, A. E. and Conolly, B. W.},
     title = {Returns to the origin for a randomized random walk},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 25},
     number = {3},
     year = {1971},
     pages = {389-395},
     zbl = {0234.60082},
     mrnumber = {319286},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1971_3_25_3_389_0}
}

Gibson, A. E.; Conolly, B. W. Returns to the origin for a randomized random walk. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 25 (1971) no. 3, pp. 389-395. http://www.numdam.org/item/ASNSP_1971_3_25_3_389_0/

Feller, W. (1957): An introduction to probability theory and its applications, Vol. 1. Wiley; New York. | MR 88081 | Zbl 0039.13201

Feller, W. (1966) : An introduction to probability theory and its applications, Vol. 2. Wiley, New York. | MR 210154 | Zbl 0138.10207

Conolly, B.W. (1971): On randomized random walks, SIAM Review, Vol. 13, N°. 1. | MR 273695 | Zbl 0215.26002

Erdelyi, A. et al. (1954): Tables of integral transforms. Mc Graw Hill, New York. | Zbl 0055.36401

Gibson, A.E. (1968): Some aspects of time dependent one dimensional random walks, Ph. D. dissertation. Virginia Polytechnic Institute, Blacksburg, Virginia.

Luke, Y.L. (1962): Integrals of Bessel functions. Mc Graw Hill, New York. | MR 141801 | Zbl 0106.04301