The paper presents some basic points of the theory of expansions in Papkovich–Fadle eigenfunctions in the polar coordinate system. Formulas for the Papkovich–Fadle eigenfunctions corresponding to the boundary value problem of the theory of elasticity for a truncated wedge with free long sides are given. Equations for determining the functions biorthogonal to the Papkovich–Fadle functions are constructed. Examples of expansions into Lagrange series, which are the basis for solving boundary value problems, are given.

1.
V. T.
Buchwald
,
J. Aust. Math. Soc.
5
,
241
257
(
1965
).
2.
B. S. R.
Rao
and
J. K.
Sridhara
,
J. Eng. Math.
4
,
361
367
(
1970
).
3.
R. W.
Little
and
T. R.
Thompson
,
J. Eng. Mech. Div.
98
,
1239
1252
(
1972
).
4.
G. A.
Grinberg
,
Prikl. Mat. Mekh.
17
,
211
228
(
1953
). [in Russian]
5.
V. V.
Vlasov
,
Method of Initial Functions in Problems of the Theory of Elasticity and Structural Mechanics
(
Stroiizdat, Moscow
,
1975
). [in Russian]
6.
M. D.
Kovalenko
,
I. V.
Menshova
,
A. P.
Kerzhaev
, and
G.
Yu
,
Z. Angew. Math. Phys.
70
,
98
(
2020
).
7.
A. F.
Leontiev
,
Series of Exponentials
(
Nauka
,
Moscow
,
1976
). [in Russian]
8.
N. I.
Muskhelishvili
,
Some Basic Problems of Mathematical Theory of Elasticity
(
Noordhoff
,
Groningen
,
1953
).
This content is only available via PDF.
You do not currently have access to this content.