practice exam b

2 line 23590 name id i continued 3 find

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Unformatted text preview: double factorial signs. = . 2 Line #: 23590. Name : ID # : ([I] continued) (3) Find the radius of convergence for the power series in (2): R= . Work for (3). 3 Line #: 23590. Name : ID # : [II] (30pts) Let ζ s denote Riemann’s zeta function. Let ε be an arbitrary positive real number. Then the improper integral +∞ ( ∗) ζs s=1+ε −1 ds is convergent. divergent. Proof: 4 Choose one. Line #: 23590. Name : ID # : [III] (30pts) (1) Recall that Γ s Γs +∞ = was defined as ts−1 e−t dt s>0 . t=0 Know that for constant real numbers p and q with p > 0 and q > 0, the following holds: 1 u=0 (1) up−1 1 − u q −1 du ΓpΓq Γ p+q = Use the abo...
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