CHU.NG TO' RANG HAM

177)

Chu.ng to' rang ham:

^{f(x) = P}

^∞

la nghi^e.m cu'a phu.o.ng trnh

^xf

⁰

^{(x)−(x+ 1)f}n!^{(x) = 0}

.

n=0

x

ⁿ⁺¹

HD gia’i:

Dung tnh ch^at D'Alembert d^e' chu.ng to' chu^o~i

^P

^∞

n!

h^o.i tu. vo.i mo.i

^x

Nhu. v^a.y ham

^{f(x) = P}

^∞

n!

xac di.nh vo.i mo.i

^x

.

x

ⁿ

Ho.n n~u.a:

^{f(x) = xP}

^∞

n! =xe

^x

⇒xf

⁰

(x)−(x+ 1)f(x) =x(x+ 1)e

^x

−(x+ 1)xe

^x

= 0, ∀x

di^eu pha'i chu.ng minh.