“Dirichlet Eta Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Dirichlet Eta Function

释义

Dirichlet Eta Function

(1)

where

, 2, ..., and

is the Riemann Zeta Function. Particular values are given in Abramowitzand Stegun (1972, p. 811). The eta function is related to the Riemann Zeta Function and Dirichlet LambdaFunction by

(2)

and

(3)

(Spanier and Oldham 1987). The value

may be computed by noting that the Maclaurin Series for

for

(4)

Therefore,


			(5)

Values for Even Integers are related to the analytical values of the Riemann Zeta Function.

is definedto be

See also Dedekind Eta Function,Dirichlet Beta Function, Dirichlet Lambda Function, Riemann Zeta Function,Zeta Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 807-808, 1972.

Spanier, J. and Oldham, K. B. ``The Zeta Numbers and Related Functions.'' Ch. 3 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 25-33, 1987.

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