Bestimmte Integrale by Wolfgang Gröbner, Nikolaus Hofreiter

By Wolfgang Gröbner, Nikolaus Hofreiter

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9b)i PfVI. -+b =0, (1212. 9c). 11) 212 212. Rationale Funktionen von :x, Va::x+b, Vcifd. 1)i 212. \p, Vb-aWtcp, Vb-a~cp)~2... (1d). l n=-1,0,1,2, ... x) a. = Jf} (3). x = ~ (b-a)\ (3). a. -a)(b-:x) Jr(1·,2·,m) (1·,2;n) (b-a \m+n) m,n=0)1,2, ... 2). b 4a) 2 ) (mtn)! 0. x a. (~). xl = V(aC+~(bc +dJ , o, bc+d >o, ae+d > a. c+d>O, be+d>O, a.

2-a1 = a y ). 16 216. :a, er()( . D( • ß Jr Jr -wn. v Jf =-l a>O, -a. 2 0 =~ 2b) 6 3a) 3b) lta) a. x = 2m a2m-t1 \ ( ~ 3 21 m+1) VY1! Wl = 0}1,2) ... ) a>0 1 (3b). a. x = (1; 2-,rn)Jr a 2m+ 2 (m+1)! 2m+2. ' m= 0,1,2, ... , a)O, (3a); a>01 (3b). n=0,112, ... , a>DJ (3a)j . . ) a>O, (3b). 0 a. d:;. = m! 2ma2m+3 m+1) (3;2; , m=0,1,2, ... , 0 a. x = (1;2;n)Jra211 n! n+1 , 0 a. 10). 20); 8b) Q. 19b). C>a>O, J a. AJtcin. Wn. a. 15b). 221 221. Elliptische Integrale in der Legendreschen kanonischen Form.

1b). ' (1b). 10); 5c) (oa). 6a) (1a ,13. 10); (6b). 3). 311 1oa:-. xe-~x}Y' =zfJ -oo 00 ~Ob) \. x >. J J o = (n- 1)! An! z3n+'f n=1,2,... , (10). A-Y)Jr K+ ,A-2Y l 0 16c) (~6). t11. 8d); 1~b) (11a). 312 ru - ~ 312. x (Laplace-Transform ation). x:x:>. A)>O, Eulersches Integral 2. 1a). Ä) > -1, (1). 1 n =0,1,2,. . , s>O, (2); s>O, (2). i_~ , 0 2s s s>O, (2). 1.! C, 335, 336)531. Vgl. IJoetsch J Theorie und Anwendung der Laplace-Transforma tion, Berlin 1931. ) e-sa. - (3). S>O, 0.. 3b). xdx = ~~K+~ 1 ) [ '\f(K+1)-W-1 ,s>O, (2, 021.

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