ada lovelace wrote a program for the analytical engine to calculate a series of bernoulli numbers.
ada lovelace wrote a program for the analytical engine to calculate a series of bernoulli numbers.
who wrote a program for the analytical engine to calculate a series of bernoulli numbers?
ada lovelace
the bernoulli numbers were discovered around the same time by the swiss mathematician jacob bernoulli, after whom they are named, and independently by japanese mathematician seki kōwa. seki's discovery was posthumously published in 1712 (; ) in his work "katsuyo sampo"; bernoulli's, also posthumously, in his "ars conjectandi" of 1713. ada lovelace's note g on the analytical engine from 1842 describes an algorithm for generating bernoulli numbers with babbage's machine . as a result, the bernoulli numbers have the distinction of being the subject of the first published complex computer program.









































section::::history.









































section::::history.:early history.
bernoulli number
faulhaber's formula was generalized by v. guo and j. zeng to a -analog .









































section::::applications of the bernoulli numbers.:taylor series.









































the bernoulli numbers appear in the taylor series expansion of many trigonometric functions and hyperbolic functions.









































bullet::::- tangent









































bullet::::- cotangent









































bullet::::- hyperbolic tangent









































bullet::::- hyperbolic cotangent









































section::::applications of the bernoulli numbers.:laurent series.









































the bernoulli numbers appear in the following laurent series :









































digamma function: formula_36









































section::::applications of the bernoulli numbers.:use in topology.
bernoulli number