The factorials and binomials have a very long history connected
with their natural appearance in combinatorial problems. Such
combinatorial‐type problems were known and partially solved even
in ancient times. The first mathematical descriptions of
binomial coefficients arising from expansions of for appeared in
the works of Chia Hsien (1050), al-Karaji (about 1100), Omar al-
Khayyami (1080), Bhaskara Acharya (1150), al‐Samaw'al (1175),
Yang Hui (1261), Tshu shi Kih (1303), Shih–Chieh Chu (1303), M.
Stifel (1544), Cardano (1545), Scheubel (1545), Peletier (1549),
Tartaglia (1556), Cardan (1570), Stevin (1585), Faulhaber
(1615), Girard (1629), Oughtred (1631), Briggs (1633), Mersenne
(1636), Fermat (1636), Wallis (1656), Montmort (1708), and De
Moivre (1730). B. Pascal (1653) gave a recursion relation for
the binomial, and I. Newton (1676) studied its cases with
fractional arguments. It was known that the factorial grows very
fast. Its growth speed was estimated by J. Stirling (1730) who
found the famous asympto