44306 transformaty6 (2)

338 Integrai. F,quations and niEiR Applications

Tablc B.2: (Continued)

	F(s)	/(O
182.	1 1 as^2 A(l-t’"')	Saw tooth wave function
183.	s	Meaviside’s unit function u(t — a)
184.	1 a ^ 1 1	Pulse function
185.	i .v( 1 — e~^as)	Step function
186.	e~^5 + e^-2ss(l - e~^s)^2	/(/) = n^2, n < / < n + 1, n = 0,1,2,...
187.	1 s( 1 - re~^s)	/(/) = r", n < 1 < n + 1, n = 0,1,2,...
188.	a(l +e~^as) a^2S^2 + 7T^2	, sin(ji7/a) 0 <l<a /(0= n 0 (> a

Table B.3: Special functions.

189.	Gamma function	r(/i) = /0°° u" ^1 e “du, n >0
190.	Beta function	B(m, n) = h! ii^m~'( 1 — uf~^idu = ^1)1 * ^, ni, n > 0 r(/;i + //)
191.	Besscl function	.r” f x^2«(•*)— 2«r(rt+ 1) i 2(2« + 2) ^ł 2.4(2/i + 2)(2/i + 4)
192.	Modified Besscl function	/nW_, Vn(or)=2nr(w + l)jl + 2(2n + 2)+. ]
193.	Error function	2 r' 2 erf(t) = —= / e “ du s/n Jo
194.	Complemcntary error function	2 r°° 2 erfc(l) = 1 - erf(t) = -^= J e " du

(Continued)

Table B.3: (Continued)

195.	Exponential integral	e~^u , £7(0 = / -du J, “
196.	Sine integral	5/(0= / -du Jo «
197.	Cosine integral	f°° cos u , Ci(t) = / -du J, u
198.	Fresncl sine integral	S(t)= f sin u^2du Jo
199.	Fresnel cosine integral	C(t)= [ cos u^2du Jo
200.	Laguerre polynomials	e' d" U0=-—ye-'), n = 0,1,2,... iv. dt"