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Bell cites several earlier publications on these numbers, beginning with Dobiński 1877 which gives Dobiński's formula for the Bell numbers. Bell called these numbers "exponential numbers"; the name "Bell numbers" and the notation B n for these numbers was given to them by Becker & Riordan 1948. [29]
The ordered Bell numbers were studied in the 19th century by Arthur Cayley and William Allen Whitworth. They are named after Eric Temple Bell, who wrote about the Bell numbers, which count the partitions of a set; the ordered Bell numbers count partitions that have been equipped with a total order.
In mathematics, the Bell series is a formal power series used to study properties of arithmetical functions. Bell series were introduced and developed by Eric Temple Bell . Given an arithmetic function f {\displaystyle f} and a prime p {\displaystyle p} , define the formal power series f p ( x ) {\displaystyle f_{p}(x)} , called the Bell series ...
Construction of the Bell triangle. The Bell numbers may also be computed using the Bell triangle in which the first value in each row is copied from the end of the previous row, and subsequent values are computed by adding two numbers, the number to the left and the number to the above left of the position. The Bell numbers are repeated along ...
The highest bell in pitch is known as the treble and the lowest the tenor. The majority of bell towers have the ring of bells (or ropes) going clockwise from the treble. For convenience, the bells are referred to by number, with the treble being number 1 and the other bells numbered by their pitch (2, 3, 4, etc.) sequentially down the scale.
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Since the Stirling number {} counts set partitions of an n-element set into k parts, the sum = = {} over all values of k is the total number of partitions of a set with n members. This number is known as the nth Bell number.
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