探索有趣的积分
Inside Interesting Integrals
Paul J. Nahin · 初版 2014 年
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既然你不可能算完所有的定积分，那么计算定积分的意义何在？本书中求解具体积分的价值并不在于我们得出的具体答案，而在于我们得出这些答案所使用的方法；这些方法可以用来计算你未来会遇到的积分。本书笔触轻松，专为学完大一微积分或高中 AP calculus、且对微分方程概念稍有了解的学生编写。书中每个结果均有完整推导。如果你着迷于……
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……范畴论，旨在教你罗威尔对不完备定理的澄清与推广。Cormen 的《算法精解》（Algorithms Unlocked），某些教材的科普版。Nahin 的《Inside Interesting Integrals》，里面有超多好玩的积分！Nahin 还写过一些关于欧拉和虚数的书，我读了一部分，看起来挺不错的。Pierce 的《信息论基础：符号、信号……
…category theory, geared towards teaching you Lawvere's clarification and generalization of the incompleteness theorems. Cormen - Algorithms Unlocked. Pop Science version of some of the textbook. Nahin - Inside interesting Integrals. Lots of fun integrations! Nahin - He also wrote some books about euler and imaginary numbers which ive partially read, they seemed good. Pierce - An introduction to information theory; symbols signals…
对于那些对数学感兴趣、尤其是想学如何攻克高难度（定）积分的人，我推荐 Paul Nahin 的这本书：《Inside Interesting Integrals》[1]。在亚马逊上评价很高，我很喜欢他的文笔。[1] https://www.amazon.com/gp/product/1493912763/ref=oh_aui_sear...
For those interested in math and particularly in learning how to attack challenging (definite) integrals, I can recommend this book by Paul Nahin: Inside Interesting Integrals [1]. It's well reviewed on Amazon and I enjoyed the writing. [1] https://www.amazon.com/gp/product/1493912763/ref=oh_aui_sear...
Boros 和 Moll 的《不可思议的积分：积分计算中的符号计算、分析与实验》（Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals），以及 Nahin 的《Inside Interesting Integrals》
"Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals" - Boros and Moll "Inside Interesting Integrals" - Nahin
我可以推荐下面这本：Nahin 写的《Inside Interesting Integrals》。这里面收录的积分往往带有数论/算术的灵感。想象一下这类东西：黎曼 zeta 函数的大量特殊值，或者调和数的偏和等等。《Irresistible…
I could suggest the following Inside Interesting Integrals, by Nahin. This contains integrals with often arithmetic inspiration. Imagine things like, lots of special values of the zeta function or partial sums of harmonic numbers and that sort of thing. Irresistible…
……在不同材料中。这些看起来相对平平无奇的定积分曾难倒过世界上一些最著名的数学家。关于它们有趣的来历，请见 [1] 和/或 [2]。[1] Paul J. Nahin, 《Inside Interesting Integrals》, Springer, 2015. 第 6.5 节, 沃森/范佩佩三重积分 (The Watson/van Peype Triple Integrals)。[2] I.J. Zucker, 《Watson 积分 70 余年》, http://www.inp.nsk.su/~silagadz/Watson_Integral.pdf
…in different materials. These, relatively, plain looking definite integrals stumped some of the world's most famous mathematicians. See [1] and/or [2] for their interesting history. [1] Paul J. Nahin, Inside Interesting Integrals, Springer, 2015. Section 6.5, The Watson/van Peype Triple Integrals. [2] I.J. Zucker, 70+ Years of the Watson Integrals, http://www.inp.nsk.su/~silagadz/Watson_Integral.pdf
有人为各种奇妙的积分写过整整一本书。George Boros 的《Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals》https://www.amazon.com/dp/0521796369/ 以及 Paul J. Nahin 的《Inside Interesting Integrals》https://www.amazon.com/Inside-Interesting-Integrals-Substitu...
Entire books have been written about curious integrals. Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, by George Boros https://www.amazon.com/dp/0521796369/ Inside Interesting Integrals, by Paul J. Nahin https://www.amazon.com/Inside-Interesting-Integrals-Substitu...