of the Falkner–Skan equation arising in boundary

For 0 < q < 1 define the symmetric q-linear operator acting on a suitable function f (x) by δf (x) = f (q1/2x) − f (q−1/2x). The q-linear initial value problem δf (x) δx = λf (x), f (0) = 1, has two entire functions Cq (z) and Sq (z) as linearly independent solutions, which are orthogonal on a discrete set. Sufficient conditions for pointwise convergence and for uniform convergence of the corresponding Fourier expansion are given. © 2005 Elsevier Inc. All rights reserved