Suppose G(r) is the generating function of a sequence (an), satisfyingG'(r) =rG(r), G(0) = 1.i. Use the ODE to show that G'(0) = 0 and use this information, together withG(0) = 1, to find ao and a₁.

Solution : G'(r)=r G(r) G'(0)=0×G(0)=0 ∫G'(r)G(r)=∫r G(r)=cer22 G(0)=1c=1 G(r)=er22 G(r)=∑i=0∞x2ii!

Answered: Suppose G(r) is the generating function…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Suppose G(r) is the generating function of a sequence (an)o, satisfying G'(r) =rG(r), G(0) = 1. i. Use the ODE to show that G'(0) = 0 and use this information, together with G(0) = 1, to find ao and a₁.