封闭形和式初步-畅读网

　　　　

封闭形和式初步

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内容简介:

我们利用一些数学工具和方法：选取适当收缩公式，利用发生函数与递推关系，和角与差角的反正切公式，剩余定理,使用微积分方法和复变函数方法，利用超几何级数的求和公式及库末 (kummer)恒等式，二阶矩阵A的n次幂An中元素a11，a12 ，a21，a22与矩阵的迹与行列式关系，利用r次单位根的性质，已知的级数公式与级数和函数公式，利用一个已知级数使用裂项法，本书给出各种不同类型数学闭形和式。

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SHOW FULL COLUMNS FROM `ls_nav` [ RunTime:0.001554s ]
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SHOW FULL COLUMNS FROM `ls_friendly_link` [ RunTime:0.001306s ]
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SHOW FULL COLUMNS FROM `ls_goods` [ RunTime:0.001832s ]
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UPDATE `ls_goods` SET `click_count` = 53 , `update_time` = 1747268805 WHERE `id` = 151502 [ RunTime:0.001044s ]
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SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 46 LIMIT 1 [ RunTime:0.000887s ]
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SHOW FULL COLUMNS FROM `ls_ad` [ RunTime:0.001353s ]
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SELECT `id`,`name` FROM `ls_goods_category` WHERE `id` = 46 LIMIT 1 [ RunTime:0.000835s ]
SELECT `a`.*,`ap`.`width`,`ap`.`height` FROM `ls_ad` `a` INNER JOIN `ls_ad_position` `ap` ON `a`.`pid`=`ap`.`id` WHERE `pid` = 11 AND `ap`.`client` = '2' AND `a`.`status` = '1' AND `a`.`del` = '0' AND `ap`.`status` = '1' AND `ap`.`del` = '0' ORDER BY `sort` DESC,`id` DESC [ RunTime:0.001059s ]
SELECT `a`.*,`ap`.`width`,`ap`.`height` FROM `ls_ad` `a` INNER JOIN `ls_ad_position` `ap` ON `a`.`pid`=`ap`.`id` WHERE `pid` = 14 AND `ap`.`client` = '2' AND `a`.`status` = '1' AND `a`.`del` = '0' AND `ap`.`status` = '1' AND `ap`.`del` = '0' ORDER BY `sort` DESC,`id` DESC [ RunTime:0.001179s ]
SELECT * FROM `ls_goods` WHERE `del` = 0 AND `status` = 1 AND `create_time` <= 1747268746 ORDER BY `create_time` DESC LIMIT 5 [ RunTime:0.536281s ]

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