lerch(VGAM)
lerch()所属R语言包：VGAM
Lerch Phi Function
勒奇披功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Computes the Lerch transcendental Phi function.
计算勒奇的先验披功能。
用法----------Usage----------
lerch(x, s, v, tolerance=1.0e-10, iter=100)
参数----------Arguments----------
参数：x, s, v
Numeric. This function recyles values of x, s, and v if necessary.
数字。此功能recyles值x，s，和v如果有必要。
参数：tolerance
Numeric. Accuracy required, must be positive and less than 0.01.
数字。精度要求，必须为正且小于0.01。
参数：iter
Maximum number of iterations allowed to obtain convergence. If iter is too small then a result of NA may occur; if so, try increasing its value.
允许以获得收敛的迭代的最大数量。如果iter是太小，则的结果NA可能发生的;如果是这样，请尝试增加它的价值。
Details
详细信息----------Details----------
The Lerch transcendental function is defined by
莱尔什超越函数定义
where |x|<1 and v != 0, -1, -2, .... Actually, x may be complex but this function only works for real x. The algorithm used is based on the relation
|x|<1和v != 0, -1, -2, ...。事实上，x可能是复杂的，但该功能仅适用于真正的x。所使用的算法是基于关系
See the URL below for more information. This function is a wrapper function for the C code described below.
的更多信息，请参见下列网址。这个函数是一个包装函数的C代码如下所述。
值----------Value----------
Returns the value of the function evaluated at the values of x, s, v. If the above ranges of x and v are not satisfied, or some numeric problems occur, then this function will return a NA for those values.
返回值的函数评估值x，s，v。如果上述范围的x和v都不满意，或会出现一些数字问题，那么这个函数将返回一个NA这些值。
警告----------Warning ----------
This function has not been thoroughly tested and contains bugs, for example, the zeta function cannot be computed with this function even though zeta(s) = Phi(x=1,s,v=1). There are many sources of problems such as lack of convergence, overflow and underflow, especially near singularities. If any problems occur then a NA will be returned.
的zeta函数，此功能还没有被彻底的测试，包含错误，例如，不能使用此功能计算，即使zeta(s) = Phi(x=1,s,v=1)。有许多来源的问题，如缺乏衔接，溢出和下溢，特别是近奇点。如果出现任何问题，然后NA将被退回。
注意----------Note----------
There are a number of special cases, e.g., the Riemann zeta-function is given by zeta(s) = Phi(x=1,s,v=1). The special case of s=1 corresponds to the hypergeometric 2F1, and this is implemented in the gsl package. The Lerch transcendental Phi function should not be confused with the Lerch zeta function though they are quite similar.
有一些特殊情况，例如，黎曼zeta函数为zeta(s) = Phi(x=1,s,v=1)。的特殊情况下s=1对应于的超几何2F1，这是实施在gsl的软件包。勒奇的先验披功能不应该被混淆的勒奇zeta函数，虽然他们是非常相似的。
（作者）----------Author(s)----------
S. V. Aksenov and U. D. Jentschura wrote the C code.
The R wrapper function was written by T. W. Yee.
参考文献----------References----------
Higher Transcendental Functions. Volume 1. McGraw-Hill, NY, USA.
参见----------See Also----------
zeta.
zeta。
实例----------Examples----------
## Not run: [＃不运行：]
s=2; v=1; x = seq(-1.1, 1.1, len=201)
plot(x, lerch(x, s=s, v=v), type="l", col="red", las=1,
main=paste("lerch(x, s=",s,", v=",v,")",sep=""))
abline(v=0, h=1, lty="dashed")
s = rnorm(n=100)
max(abs(zeta(s)-lerch(x=1,s=s,v=1))) # This fails (a bug); should be 0[失败（错误）应为0]
## End(Not run)[＃（不执行）]
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
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发表于 2012-10-1 15:40:34
