“Legendre chi function”的意思、由来-开放百科全书

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Legendre chi function

释义

Identities
Integral relations
References

In mathematics, the Legendre chi function is a special function whose Taylor series is also a Dirichlet series, given by

As such, it resembles the Dirichlet series for the polylogarithm, and, indeed, is trivially expressible in terms of the polylogarithm as

The Legendre chi function appears as the discrete Fourier transform, with respect to the order ν, of the Hurwitz zeta function, and also of the Euler polynomials, with the explicit relationships given in those articles.

The Legendre chi function is a special case of the Lerch transcendent, and is given by

Identities

Integral relations

References

{{mathworld|urlname=LegendresChi-Function |title=Legendre's Chi Function}}
Djurdje Cvijović and Jacek Klinowski, "Values of the Legendre chi and Hurwitz zeta functions at rational arguments", Mathematics of Computation 68 (1999), 1623-1630.
{{note_label|Cvijovic2006||}}{{cite journal|author=Djurdje Cvijović|year= 2006

|url=http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WK2-4MG1X3C-6&_user=1793225&_coverDate=11%2F30%2F2006&_alid=512412473&_rdoc=2&_fmt=summary&_orig=search&_cdi=6894&_sort=d&_docanchor=&view=c&_acct=C000053038&_version=1&_urlVersion=0&_userid=1793225&md5=d64e4c1e1d59beb223eefd865b64e422|title=Integral representations of the Legendre chi function|journal= Journal of Mathematical Analysis and Applications
|volume= 332
|issue= 2
|pages= 1056–1062
|accessdate=December 15, 2006|doi=10.1016/j.jmaa.2006.10.083|arxiv=0911.4731}}{{dead link|date=March 2019|bot=medic}}{{cbignore|bot=medic}}

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