transformaty5 (2)

336 Integral Ecjuations and their Applic ations

Table R.2: (Continucd)

	F(s)	fd)
153.	e~xs/as^i +bs + c — e-(bx/2y/a)e-Jaxs	(0 0 < / < y/ax ^1 V 4 a ( s/b^2-4ca n- M 2« " ^aX )
154.	1 . Cl — sin - yJS S	sinh s/Tat sin s/lat sfnt
155.	1 . a —7= sin -Sy/S s	cosh s/lat sin s/lat sfan
156.	1 a —7= COS -Sy/S S	cosh s/lat cos s/lat sfnt
157.	1 a —7= cos -Sy/S s	sinh s/lat cos s/lat sfan
158.	, s^2 — as — b tan ^1- ab	e^al - 1 -sin bt t
159.	las ‘^an .v^2 - a^2 + b^2	1 . - sin at cos bt t
160.		e~^r
161.	sinh.v.v s sinh sa	^x . ^2 V'oo (-■)" . nnx nnt - H— 2^/i-1-sin-cos — a n ^7,-1 n a a
162.	sinh sx scosh sa	^4 v-co (-•)" . (2/i — 1 )nx . (2/1 - 1 )nt 2-h-i , ^Sln-^-sin- n ^1 2// — 1 la la
163.	cosh sx s sinlv.sc/	^1 X. ^2 (^-1)^nnnx ■ ^nnt - + - Zw,-1-cos-sin- a n n a a
164.	cosh sx s cosh sa	, , ^4 v-oo (-1)" (2/i — l)jr.v (2// — 1)7T/ n^"-' l,i-l la la
165.	sinh .v.r s^2 sinli sa	xt la ^ (-1)" , nnx . nnt + 2 2^n=| 2 ^S1Ił Sln - a n^2 " ' n^2 a a
166.	sinh sx s^2 cosh sa	8// (-1)" (2/i—l)7rx (2/1—1)717
		^+ n^2 ^^n~^l (2/i— l)^2 S 1 2n ^C°^S 2</

(Continued)

Table B.2: (Continued)

	F(s)	m
167.	cosh xx s^2 sinh sa	l^2 2a „oo (-1)" nnx f nnl\ — + E^-i r- cos- 1 - cos — la n^1 n^2 a \ aj
168.	cosh sx s^2 cosh sa	. , ^(-'^)n co- (^2”—^1)^7rjc „j (^2n—1>7r<
		^/+ 7r^2^'"^=l(2n-l)^2 °- 2u 2a
169.	cosh sx s^3 cosh sa	l . , . , 16a^2 ^oo ("O" -(/^2 +x^2 —a^2) ^3 E„=l (2„_ ,)3 (2/i — 1 )jtjc (2/i — l)7rt x cos---cos _la._2a-
170.	sinhx./ś sinha^/s	% i (-\)^nne~^nlnhlal sin — a2 y > a
171.	cosh*^ cosh a^/s	iL (—l)^n-,(2/i - i^-a/i-O^W tr (2n - \)nx x cos--- _la_—
172.	sinh Xy/s Jscos\\aJs	- E^-t (—I)'^,-1e^_*^2n-,)!’^r2,/4‘^l2 sin ^(2"~J^)7r-
173.	coshjr y/s jsśinha^ś	I + - V~1 (-1 )"<r'^,J’^rJ'^/a2 cos — a a ^n o
174.	s\nhxjś ss\nha^/s	1 M /i a n n a
175.	coshx,/f s cosh ajs	^1+; ss.
176.	sinh a^/5 s^2 sinh a^/s	7 + ^d,^( j^}(l c-W)sin fl
177.	coshxy/s s^2 cosh a s/s	1. 2 2\ i t -(x^2-a^2) + f-^3-En=l x e-(2 n-\W,4o\0^^2n-'^)nX ^x(2 /.-n^3 2fl
178.	ś-(?)	Triangular wavc function
179.	;-(f)	Square wave function
180.	na t_/^as' a^2s^2 + n^1 C°^thV 2	Rectificd sine wave function
181.	na (<j^2s^2+7T^2)(1 — e^-"^5	Ilalf-rectificd sine wave function

(Conlinued)