释义 |
Maclaurin SeriesA series expansion of a function about 0,
 | (1) |
named after the Scottish mathematician Maclaurin. Maclaurin series for common functions include | (2) |  | (3) |  | (4) |  | (5) |  | (6) |  | (7) |  | (8) |  | (9) |  | (10) |  | (11) |  | (12) |  | (13) |  | (14) |  | (15) |  | (16) |  | (17) |  | (18) |
 | (19) |  | (20) |  | (21) |  | (22) |  | (23) |  | (24) |  | (25) |  | (26) |  | (27) |  | (28) |  | (29) |  | (30) |  | (31) |  | (32) |  | (33) |  | (34) | The explicit forms for some of these are | (35) |  | (36) |  | (37) |  | (38) |  | (39) |  | (40) |  | (41) |  | (42) |  | (43) |  | (44) |  | (45) | where are Bernoulli Numbers and are Euler Numbers.See also Alcuin's Sequence, Lagrange Expansion, Legendre Series, Taylor Series References
Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 299-300, 1987.
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