tgamma

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Langue: ja

Version: 2004-11-15 (openSuse - 09/10/07)

Section: 3 (Bibliothèques de fonctions)

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tgamma, tgammaf, tgammal - ËÜÅö¤Î¥¬¥ó¥Þ´Ø¿ô

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#include <math.h>

double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);

-std=c99 ¤Ç¥³¥ó¥Ñ¥¤¥ë¤·¡¢-lm ¤Ç¥ê¥ó¥¯¤¹¤ë¡£

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 Gamma(x) = t^(x-1) e^-t dt ¤Î 0 ¤«¤é̵¸ÂÂç¤Þ¤Ç¤ÎÀÑʬ

¤³¤Î´Ø¿ô¤ÏÀµ¤Ç¤Ê¤¤À°¿ô¤ò½ü¤¯¤¹¤Ù¤Æ¤Î¼Â¿ô¤ËÂФ·¤ÆÄêµÁ¤µ¤ì¤Æ¤¤¤ë¡£ ÈóÉé¤ÎÀ°¿ô m ¤Ë´Ø¤·¤Æ¡¢°Ê²¼¤¬À®Î©¤¹¤ë:


 Gamma(m+1) = m!

¤è¤ê°ìÈÌŪ¤Ë¤Ï¡¢¤¹¤Ù¤Æ¤Î x ¤Ë´Ø¤·¤Æ°Ê²¼¤¬À®Î©¤¹¤ë:


 Gamma(x+1) = x * Gamma(x)

¤µ¤é¤Ë¡¢¶Ë¤ò½ü¤¯¤¹¤Ù¤Æ¤Î x ¤Ç¼¡¼°¤âÀ®Î©¤¹¤ë:


 Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)

¤³¤Î´Ø¿ô¤Ï¡¢°ú¤­¿ô x ¤ËÂФ¹¤ë¥¬¥ó¥Þ´Ø¿ô¤ÎÃͤòÊÖ¤¹¡£ ¤³¤Î´Ø¿ô¤Ï¡ÖËÜÅö¤Î (true) ¥¬¥ó¥Þ´Ø¿ô¡×¤È¸Æ¤Ð¤ì¤ë¡£ ¤Ê¤¼¤Ê¤é¡¢ gamma(3) ¤È¤¤¤¦´Ø¿ô¤¬¤¹¤Ç¤Ë¸ºß¤·¡¢Â¾¤ÎÃͤòÊÖ¤¹¤«¤é¤Ç¤¢¤ë¡£

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¥¨¥é¡¼¤ò¥Á¥§¥Ã¥¯¤¹¤ë¤¿¤á¤Ë¤Ï¡¢¤³¤ì¤é¤Î´Ø¿ô¤ò¸Æ¤Ó½Ð¤¹Á°¤Ë errno ¤ò 0 ¤Ë¥»¥Ã¥È¤·¡¢ feclearexcept(FE_ALL_EXCEPT) ¤ò¸Æ¤Ù¤Ð¤è¤¤¡£ ´Ø¿ô¼Â¹Ô¸å¤Ë¡¢ errno ¤¬ 0 °Ê³°¤«¡¢ fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) ¤¬ 0 °Ê³°¤Ê¤é¤Ð¡¢¥¨¥é¡¼¤¬È¯À¸¤·¤¿¤³¤È¤¬Ê¬¤«¤ë¡£

x ¤¬Â礭¤¹¤®¤ë¾ì¹ç¡¢range error ¤¬È¯À¸¤¹¤ë¡£ x ¤¬ 0 ¤Ç¤¢¤ë¾ì¹ç¡¢pole error ¤¬È¯À¸¤¹¤ë¡£ x ¤¬Éé¤ÎÀ°¿ô¤Î¾ì¹ç¤Ë¤Ï domain error (¤â¤·¤¯¤Ï pole error) ¤¬È¯À¸¤¹¤ë¡£

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C99.

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gamma(3), lgamma(3)