Znn3bq.jpeg
²é¿´: 1614  |  »Ø¸´: 4

iάÊý

ľ³æ (ÕýʽдÊÖ)

[ÇóÖú] Éæ¼°Ù¤Âíº¯ÊýµÄ¼¶Êý¼«ÏÞ

Èçͼ£¬GammaÊÇÙ¤Âíº¯Êý£¬a>0,aÕýÏòÇ÷ÓÚ0¡£Ð»Ð»¸÷λ£¡

Éæ¼°Ù¤Âíº¯ÊýµÄ¼¶Êý¼«ÏÞ
Éæ¼°Ù¤Âíº¯ÊýµÄ¼¶Êý¼«ÏÞ.png
»Ø¸´´ËÂ¥

» ²ÂÄãϲ»¶

ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

hank612

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

͵͵ÎÊÒ»ÏÂ, In[60]ÖÐÄǸö¼¶ÊýÔÚa=0+´¦½¥½üÕ¹¿ªÊDz»ÊǵÈÓÚ(asymptotic expansion)

?

ÎÒÖ»ÖªµÀµÚÒ»ÏîºÍµÚ¶þÏîÓëÄã¼ÆËãµÄ¼«ÏÞֵǡºÃÎǺÏ, ÓÉ"Ò»Éú¶þ,¶þÉúÈý,ÈýÉúÍòÎï" , ºóÃæµÄÏîÓ¦¸ÃÒ²ÊǶԵÄ. Õ¹¿ªÊ½À´×Ô  http://dlmf.nist.gov/10.2 (¼ÓÉÏһЩ±äÐÎ)

Äã¿ÉÒÔ°ïæËãһϵÚÈýÏîÊÇ·ñÊÇ:
??

лл
We_must_know. We_will_know.
2Â¥2016-06-09 05:47:42
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

hank612

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
2Â¥: Originally posted by hank612 at 2016-06-09 05:47:42
͵͵ÎÊÒ»ÏÂ, InÖÐÄǸö¼¶ÊýÔÚa=0+´¦½¥½üÕ¹¿ªÊDz»ÊǵÈÓÚ(asymptotic expansion)

\sqrt{2\pi}a^{-\frac{1}{4}}(1+\sum_{k=1}^{\infty}\frac{a^k}{k!}\prod_{m=1}^k ((2k-1)^2-\frac{1}{4}))?

ÎÒÖ»ÖªµÀµÚÒ»ÏîºÍµÚ ...

¸üÕýһϴíÎó:

In[60]ÖÐÄǸö¼¶ÊýÔÚa=0+´¦½¥½üÕ¹¿ªÊDz»ÊǵÈÓÚ

We_must_know. We_will_know.
3Â¥2016-06-09 05:59:14
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

iάÊý

ľ³æ (ÕýʽдÊÖ)

ÒýÓûØÌû:
2Â¥: Originally posted by hank612 at 2016-06-09 05:47:42
͵͵ÎÊÒ»ÏÂ, InÖÐÄǸö¼¶ÊýÔÚa=0+´¦½¥½üÕ¹¿ªÊDz»ÊǵÈÓÚ(asymptotic expansion)

\sqrt{2\pi}a^{-\frac{1}{4}}(1+\sum_{k=1}^{\infty}\frac{a^k}{k!}\prod_{m=1}^k ((2k-1)^2-\frac{1}{4}))?

ÎÒÖ»ÖªµÀµÚÒ»ÏîºÍµÚ ...

лл´óÉñ£¡µÚÈýÏîÄǸöϵÊýȷʵÊÇÒ»ÑùµÄ¡£
4Â¥2016-06-09 12:12:27
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

hank612

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
4Â¥: Originally posted by iάÊý at 2016-06-09 12:12:27
лл´óÉñ£¡µÚÈýÏîÄǸöϵÊýȷʵÊÇÒ»ÑùµÄ¡£...

ÈýÏÊÇÏÓÉÙÁËЩ°¡¡£ Äܲ»ÄÜËã¸ö6£¬7 ÏҲÐí¹æÂɾͻá×Ô¼ºÌø³öÀ´£¿
We_must_know. We_will_know.
5Â¥2016-06-29 23:30:32
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ iάÊý µÄÖ÷Ìâ¸üÐÂ
×î¾ßÈËÆøÈÈÌûÍÆ¼ö [²é¿´È«²¿] ×÷Õß »Ø/¿´ ×îºó·¢±í
[¿¼ÑÐ] ¼ÆËã»ú22408 281·Ö£¬Çóµ÷¼Á +7 17715607211 2026-04-06 7/350 2026-04-12 00:43 by xuxiang
[¿¼ÑÐ] 268Çóµ÷¼Á +3 ÄãºÃtg 2026-04-05 5/250 2026-04-11 16:45 by Delta2012
[¿¼ÑÐ] 274Çóµ÷¼ÁÇóµ÷¼Á +11 Jachenbingoo 2026-04-06 14/700 2026-04-11 11:37 by ×ÏêØ×ÏÆå
[¿¼ÑÐ] 298Çóµ÷¼Á +5 ²ÐºÉÐÂÁø 2026-04-07 5/250 2026-04-11 11:02 by ×ÏêØ×ÏÆå
[¿¼ÑÐ] ²ÄÁÏÓ뻯¹¤µ÷¼Á 10+11 ÏÂÒ»Õ¾Éϰ¶@ 2026-04-10 36/1800 2026-04-11 10:26 by 89436494
[¿¼ÑÐ] 22408 327·ÖÇóµ÷¼Á +4 ÔÏ·çkon 2026-04-10 4/200 2026-04-11 09:51 by Öí»á·É
[¿¼ÑÐ] ¸´ÊÔµ÷¼Á +9 »ý¼«ÏòÉÏ£» 2026-04-10 11/550 2026-04-11 09:25 by Öí»á·É
[¿¼ÑÐ] Ò»Ö¾Ô¸¶«±±´óѧ¿ØÖƹ¤³Ì085406Êý¶þÓ¢¶þ385£¬Çóµ÷¼Á +8 Ezra_Zhang 2026-04-09 8/400 2026-04-11 09:15 by Öí»á·É
[¿¼ÑÐ] 083200 305·Ö Çó¶þÂÖµ÷¼Á ²»½ÓÊÜ¿çרҵ +9 Claireyyyy 2026-04-09 10/500 2026-04-10 21:21 by Claireyyyy
[¿¼ÑÐ] Ò»Ö¾Ô¸»¦9£¬326ÉúÎïѧÇóÏà¹Ø×¨Òµµ÷¼Á +4 Áõīī 2026-04-09 4/200 2026-04-10 12:07 by pengliang8036
[¿¼ÑÐ] »úе»¹Óл¹ÓÐÃû¶îÂð£¿Ì«ÄÑÁË +6 ЦЦԬ 2026-04-10 6/300 2026-04-10 11:54 by ¸ßά´º
[¿¼ÑÐ] µ÷¼ÁÉêÇë086000Ò»Ö¾Ô¸Î÷±±Å©ÁֿƼ¼´óѧÉúÎïÓëÒ½Ò©320·Ö-±¾¿ÆÆë³¹¤Òµ´óѧ +3 ÃÀÃÀŮʿ 2026-04-09 3/150 2026-04-10 10:31 by liuhuiying09
[¿¼ÑÐ] ²ÄÁÏ»¯¹¤×Ü·Ö334Çóµ÷¼Á +16 Riot2025 2026-04-08 17/850 2026-04-09 20:19 by maddjdld
[¿¼ÑÐ] »¯Ñ§¹¤³ÌÓë¼¼Êõרҵһ־Ը¹þ¹¤³Ì 291·ÖBÇø ¹ú¼Ò¼¶´ó´´¸ºÔðÈË ÓÐÒ»×÷ÂÛÎÄ +13 Emmy~ 2026-04-09 13/650 2026-04-09 14:47 by onlyÖÜ
[¿¼ÑÐ] 086004 Çóµ÷¼Á 309 +7 Yin DY 2026-04-08 7/350 2026-04-09 13:59 by Delta2012
[¿¼ÑÐ] ÉúÎïѧ308·ÖÇóµ÷¼Á£¨Ò»Ö¾Ô¸»ª¶«Ê¦´ó£© +13 ÏàÐűػá¹ââÍòÕ 2026-04-06 16/800 2026-04-09 13:54 by ÐìÁ¼°×ü´óÏÀ
[¿¼ÑÐ] 334Çóµ÷¼Á +16 Riot2025 2026-04-08 17/850 2026-04-09 09:28 by wdyheheeh
[¿¼ÑÐ] 275 Çóµ÷¼Á +8 Lei812514 2026-04-07 8/400 2026-04-08 12:46 by chemisry
[¿¼ÑÐ] 085602µ÷¼Á ³õÊÔ×Ü·Ö335 +10 19123253302 2026-04-05 10/500 2026-04-07 15:23 by СÇÇͬѧya
[¿¼ÑÐ] Ò»Ö¾Ô¸ËÕÖÝ´óѧ²ÄÁϹ¤³Ì£¨085601£©×¨Ë¶ÓпÆÑо­ÀúÈýÏî¹ú½±Á½¸öʵÓÃÐÍרÀûÒ»ÏîÊ¡¼¶Á¢Ïî +11 ´ó»ðɽС»ðɽ 2026-04-05 11/550 2026-04-06 22:55 by yunlongyang
ÐÅÏ¢Ìáʾ
ÇëÌî´¦ÀíÒâ¼û