Every real number , has an essentially unique expansion as a Pierce series :
@article{JTNB_1991__3_1_43_0, author = {P. Erd\"os and J. O. Shallit}, title = {New bounds on the length of finite pierce and {Engel} series}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {43--53}, publisher = {Universit\'e Bordeaux I}, volume = {3}, number = {1}, year = {1991}, zbl = {0727.11003}, mrnumber = {1116100}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_1991__3_1_43_0/} }
TY - JOUR AU - P. Erdös AU - J. O. Shallit TI - New bounds on the length of finite pierce and Engel series JO - Journal de théorie des nombres de Bordeaux PY - 1991 SP - 43 EP - 53 VL - 3 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_1991__3_1_43_0/ LA - en ID - JTNB_1991__3_1_43_0 ER -
P. Erdös; J. O. Shallit. New bounds on the length of finite pierce and Engel series. Journal de théorie des nombres de Bordeaux, Volume 3 (1991) no. 1, pp. 43-53. https://jtnb.centre-mersenne.org/item/JTNB_1991__3_1_43_0/
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and ,