Geodesic
On the representation by Dirichlet series of analytic functions in a~closed convex polygonal region
Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 133-144

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Let $\overline D$ be a closed convex polygonal region. It is shown that, for any function $f(z)$ analytic in the open region $D$ and continuous together with its first derivative in $\overline D$, a Dirichlet series can be constructed (its exponents depend only on $D$) that converges to $f(z)$ everywhere in $\overline D$ except, possibly, at its vertices. 
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     author = {A. F. Leont'ev},
     title = {On the representation by {Dirichlet} series of analytic functions in a~closed convex polygonal region},
     journal = {Izvestiya. Mathematics },
     pages = {133--144},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_1_a7/}
}
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A. F. Leont'ev. On the representation by Dirichlet series of analytic functions in a~closed convex polygonal region. Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 133-144. http://geodesic.mathdoc.fr/item/IM2_1974_8_1_a7/