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hank612

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ÃϾ§¾§345(feixiaolin´ú·¢): ½ð±Ò+10 2014-10-31 07:44:52
http://www.math.hawaii.edu/~pavel/bernoulli.pdf

ÎÒÕÕ³­Ò»±é, Euler µÄÖ¤Ã÷¼òµ¥,Éî¿Ì, ÁîÈËÏëÍü¶¼ÄÑ.

¶¨Òå

¶¨Òå Bernoulli Êý.

ÓÉÓÚÊÇżº¯Êý, ËùÒÔ.

ǰ¼¸¸ö·ÇÁãµÄBernoulli ÊýÊÇ:

Euler¸æËßÎÒÃÇ, .

Õâ¸öÊǸ´±äº¯ÊýÖеļòµ¥Á·Ï°. ÒòΪ×ó±ß¼õÈ¥ÓÒ±ßÊǸöÕûº¯Êý, ÔÚÎÞÇîÔ¶µãÊÕÁ²,ÓÉPicard¶¨ÀíÖªµÀÕâ¸ö²îÊǸö³£Êýº¯Êý. ¸Ã³£Êýº¯ÊýÔÚz=0´¦È¡ÖµÎªÁã. ËùÒÔµÈʽ³ÉÁ¢.

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2Â¥2014-10-31 01:12:39
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zaq123321

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Amazing.

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hank612

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4Â¥2014-10-31 08:20:30
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ÒýÓûØÌû:
4Â¥: Originally posted by hank612 at 2014-10-31 08:20:30
¶Ô²»Æð ÎÒûעÒâµ½ÄãÖ»Çó¶ÔÆæÊýµÄËĴη½µÄÇóºÍ.
\frac{\pi^4}{90}=\sum_{k=0}^{\infty}\frac{1}{(2k+1)^4}+\sum_{k=1}^{\infty}\frac{1}{(2k)^4}=\sum_{k=0}^{\infty}\frac{1}{(2k+1)^4}+\frac{1}{2^4}\cdot  ...

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½ð³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
2Â¥: Originally posted by hank612 at 2014-10-31 01:12:39
http://www.math.hawaii.edu/~pavel/bernoulli.pdf

ÎÒÕÕ³­Ò»±é, Euler µÄÖ¤Ã÷¼òµ¥,Éî¿Ì, ÁîÈËÏëÍü¶¼ÄÑ.

¶¨Òå\zeta(2m)=\sum_{n=1}^{\infty}\frac{1}{n^{2m}}=\frac{1}{1^{2m}}+\frac{1}{2^{2m}}+\frac{1}{3^{ ...

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