请输入您要查询的字词:

 

单词 GeneratingFunctionForTheReciprocalCatalanNumbers
释义

generating function for the reciprocal Catalan numbers


The series

1+x+x22+x35+x414+x542+x6132+x7429+

whose coefficients are the reciprocal of the Catalan numbersDlmfMathworldPlanetmath (2nn)n+1, has as a generating function

2(4-x(8+x)+12xarctan(x4-x))(4-x)5

To deduce such a formula the easy way, one starts from the generating function of the reciprocal central binomial coefficientsMathworldPlanetmath and having into account the relation

ddx(xn+1(2nn))=(n+1)xn(2nn)

for each term in the corresponding series and applied to the functionMathworldPlanetmath in the region of uniform convergenceMathworldPlanetmath.Another method is almost exaclty the same like in the derivation of the generating function for the reciprocal central binomial coefficients.

随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 9:11:06