id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-282	Papanicolaou, Vassilis G.; Kallitsi, Eva; Smyrlis, George	Entire solutions for the heat equation	2021	25	.pdf	application/pdf	11196	591	83	(3.64) Then, from our assumption for the order and type of f(z), the integral in the right- hand side of (3.64) is entire in (t, z), satisfies the heat equation for every t, z ∈ C (e.g., by analytic continuation) and it is clear from (3.64) that F (0, z) = f(z). Using (1.5) in (1.1) yields F (t0 + t, z0 + z) = ∑ j,k≥0 ∂2j+kz F (t0, z0) j!k! tjzk, t, z ∈ C. (1.6)	cache/ejde-282.pdf	txt/ejde-282.txt