## Convex? (Solved)

Summary: For each $N \in \NN$ define the function $f_N: \RR_+^N \to \RR_+$ by $f_N(x_1, \ldots, x_N) := \int_0^1 (1 - \prod_{i=1}^N (1-t^{x_i})) dt/t$. It is desired to know whether $f_N$ is convex.

Classification: Primary, classical analysis; Secondary, convex functions

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**Jonathan Borwein**

CECM

Department of Mathematics and Statistics

Simon Fraser University

Burnaby, BC, V5A 1S6

Canada

e-mail: jborwein@cecm.sfu.ca

**Ian Affleck**

CECM

Simon Fraser University

**Roland Girgensohn**

GSF-Forshungszentrum

Institut für Biomathematik und Biometrie

Neuherberg, Germany**Download Solution**[PDF]

**Ian Affleck**

CECM

Department of Mathematics and Statistics

Simon Fraser University

Burnaby, BC, V5A 1S6

Canada

e-mail: anghelv@aecl.ca**Download Solution**[PDF]

**Jonathan Borwein**

CECM

Department of Mathematics and Statistics

Simon Fraser University

Burnaby, BC, V5A 1S6

Canada

e-mail: jborwein@cecm.sfu.ca

**Omar Hijab**

Department of Mathematics

Temple University

Philadelphia, PA 19122, USA

e-mail: hijab@math.temple.edu