“Lambert Series”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lambert Series

释义

Lambert Series

A series of the form

(1)

for

. Then

(2)

where

(3)

Some beautiful series of this type include

			(4)
			(5)
			(6)
			(7)
			(8)

where

is the Möbius Function,

is the Totient Function,

is the number of divisors of

is the Divisor Function,and

is the number of representations of

in theform

where

and

are rational integers (Hardy and Wright 1979).

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Number Theoretic Functions.'' §24.3.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 826-827, 1972.

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 257-258, 1979.

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