On Lidstone's Series and Two-Point Expansions of Analytic Functions

A chronology of interpolation: from ancient astronomy to modern signal and image processing

“…; m, with usually k = 1, is also called osculatory or osculating interpolation [25], [26], [31]. The problem corresponding to E = I , with I the (m+1)2(m+1) unit matrix, was studied by Abel [74] and later by Gontcharoff and others [26], [75], [76] and, finally, we mention the two-point interpolation problem studied by Lidstone [26], [76]- [78] for which E is a 2 2(k + 1) matrix with e = 1 for all j even.…”

Behandlung eines Whittakerschen Mehr-Punkte-Problems mit Perronschen Summengleichungen

“…[13] S. 452 bzw. [10] S. 109) auch ,,unvollst~indige" mit der Eigenschaft, dab sich die zugeh6rigen L6sungen f von (11) nicht als Reihen yon Standardpolynomen darstellen lassen.…”

“…[13] Theorem 1, S. 455 und [14]). In Anleknung an seine Terminologie bezeichen wir obige Aufgabe als ,,Mehr-PunkteProblem".…”

“…die Existenz einer L6sung yon(13) sichert und dab sich diese mit sog. Lidstoneschen Reihen darstellen l~il3t.…”

Eigenvalues of complementary Lidstone boundary value problems

“…The Lidstone interpolation has a long history from 1929 when Lidstone [8] introduced a generalization of Taylor's series that approximates a given function in the neighborhood of two points instead of one. Further characterization can be found in the study of [9][10][11][12][13][14][15][16]. More research on Lidstone interpolation as well as Lidstone spline is seen in [1,[17][18][19][20][21][22][23].…”