Question

A theorem about functions with this property uses a sequence of functions E-sub-n, the nth of which equals one minus z all times e to the partial sum of z to the k over k; such functions are called elementary factors. Given a sequence with moduli tending to infinity, there exists a function with this property whose zeroes are precisely that sequence. The Taylor coefficients, a-sub-n, (15[1])of functions with this property satisfy the condition that the lim-sup (“lim soup”) of the absolute value of a-sub-n (-5[1])to the power of one over n is (*) zero. The Hadamard factorization theorem applies to functions with this property whose Cauchy–Hadamard radius is infinity. Non-constant functions with this property can miss at most one point (10[1])by Picard’s little theorem. (10[1]-5[2])Bounded (10[1])functions with this property are constant by Liouville’s (10[1])theorem. (10[1])For 10 points, name this property of functions that are holomorphic everywhere on the complex plane. ■END■ (10[1]0[2])

ANSWER: entire [accept answers indicating that the function is everywhere differentiable, everywhere analytic, or everywhere holomorphic until “everywhere” is read; prompt on holomorphic until read; prompt on complex differentiable or analytic by asking “what is this called for complex function?”]
<Tim Morrison, Other Science - Math>
= Average correct buzz position

Summary

2023 Chicago Open08/05/2023Y1070%10%30%119.14

Buzzes

PlayerTeamOpponentBuzz PositionValue
Swapnil GargEvans Hall destruction awaitersI prefer really not to speak. If I speak I’m in big trouble6515
Jeremy CummingsHang et al., Robert BrowningDon't be Afraid, the Clown's Afraid Too82-5
Conor Thompson[moderator voice] yes that is so tenpointscore! is your team feeling bonuspilled?Quasicrystal Silence11710
Mike SoriceTeam Name Think DetailSaint Peter Andre 3000121-5
Adam FineThe Catastrophic Implosion of Packet SubThe anti-STOON-dahl cabal (the tall Keyal et al.)12110
Vishwa ShanmugamIn Search of Things PastI would prefer not to121-5
Geoffrey ChenThe Plague (anime)" was redirected to: "Oran High School Host ClubBHSU12210
Jerry VinokurovTeach Us to Outgrow Our Ladnessremembrance of lost time13010
Eric MukherjeeCurse you, Periplus the Platypus!Romanos IV Diogenes’ Macaroni Grill13110
Kevin WangI would prefer not toIn Search of Things Past1480
Shahar SchwartzSaint Peter Andre 3000Team Name Think Detail1480
Rein OtsasonThe Canadianswave2: trimming membership codes 9655377758gp14810