1、 x s s 9 赵纬经,王贵君(? = S v S ,? null 300387)K null 1 : t 4 v s 9 5 , n 5 Y V a M | x s , x s ,V 7 P s 9 5 F % , 7 B t + y s 9 4 B r Z E .1 o M : x s ;null f ;Bf m s | :O172.2null null null null D S M :Anull null null null c I | :1001- 7542(2008)01- 0005- 041null ! M s s 9 5 ,Y S E 5 p f , d null D G T
2、 / K 9 . B t + A 5 “ , H 9 M 9 , w / F Z E ) .3 ; v s ! S sI ,? C s 9 5 d 0),B(p, q) = 10xp-1(1 -x)q-1dx(p 0, q 0)d x s , - nullf , Bf . 1null null f / 3H :(1)null(s) l s 0 = O V ;(2) w T null(s+ 1) = snull(s),+ Y n Z+H null(n+ 1) = n!;(3) nullf “ s % 0, - 1, - 2(2) :B(p,q) = B(q,p). 3null null f Bf
3、 1 “ :B(p, q) = null(p)null(q)null(p + q) (p 0, q 0). 5 1( T ) null s % 0,1,2null - n+ 12 = (- 1)n2n(2n- 1)! null. 5 26 nullnull20sinmxcosnxdx= 12B m+ 12 , n+ 12 ,(m - 1,n - 1).2null s 9 : 4 + M n 3 I k s k ,3 ? C s 9 B 1 ,i O s5 “ Z E + a 4 v a/ F ./ , Y V s 9 5 , 8 ) P x s 9 s , N A N Zl :2007- 12
4、- 10T e :u (1984- ), 3 , 2 ,q B , V 3 , Z _ : s . L , (1962- ), 3 , Y ,q B , q , Z _ : s .2008 M 1 null null null null null null null null Z = S v (自然科学版)JournalofQinghaiNormalUniversity(NaturalScience) null null null null null null null null2008No.1E , V P 5 4 e ,Y . , q s + #0 e- x2dx # w 1) null
5、7 t = 11+ xm,5 dx = - 1mt-1- m(1-t)m-1dt, 3 5 1+ #0 11+ xmdx = 1m+ #0 t- 1m(1- t)1m-1dt= 1mB 1- 1m, 1m= 1mnull 1- 1m null 1m = nullmsim nullm4 N 5 , 4 ? C , m= 3 m= 4 H , | 9 n s , ,+ #0 11+ x3dx = null3sin null3= 2null3 3,+ #0 11+ x4dx = null4sin null4= null2 2.2.3null s 9 1 s 9 s ! = ,9 3 I k I =
6、B , t 5 “ T / ,/ F - 1, s10r2!+2+2#-11+ r2 dr l ,7 s + #1r2!+ 2+ 2#-11+ r2 dr l O 2!+ 2+ 2#- 1 . , , a . s l 5 M. : ,2002.5null . M f M( ). : ,2003.6null , , . s M.(/ ). : ,2000.Soving definite integral caculation by using euler integralZHAO Weinulljing,WANG Guinulljun(School ofMathematicsScience,Ti
7、anjingNormalUniversity,Tianjin 300387,China)Abstract: Inthis paper,aiming at solvingsomeverydifficult definite integral caculation problems,these probnulllemsaretransformedintoEuler integralthroughcertaintransformationatfirst,thentheseproblemsaresolved easilybyusingsomeofpropertiesof Euler integral,so it provides an effectivemethod of solvingsomespecialtpyesof definiteintegralcaculation tous.Key words: Euler integral;null- function; B- function8 null null null null null null null null null null null null null null Z = S v (自然科学版) null null null null null null null null null null 2008年
