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
).
https://doi.org/10.1017/S1446788700026811
Google Scholar
Crossref
Search ADS
 
2.
B. S. R.
 
Rao
 and
J. K.
 
Sridhara
,
J. Eng. Math.
 
4
,
361
–
367
(
1970
).
https://doi.org/10.1007/BF01534983
Google Scholar
Crossref
Search ADS
 
3.
R. W.
 
Little
 and
T. R.
 
Thompson
,
J. Eng. Mech. Div.
 
98
,
1239
–
1252
(
1972
).
https://doi.org/10.1061/JMCEA3.0001665
Google Scholar
Crossref
Search ADS
 
4.
G. A.
 
Grinberg
,
Prikl. Mat. Mekh.
 
17
,
211
–
228
(
1953
). [in Russian]
Google Scholar
 
5.
V. V.
 
Vlasov
,
Method of Initial Functions in Problems of the Theory of Elasticity and Structural Mechanics
(
Stroiizdat, Moscow
,
1975
). [in Russian]
Google Scholar
 
6.
M. D.
 
Kovalenko
,
I. V.
 
Menshova
,
A. P.
 
Kerzhaev
, and
G.
 
Yu
,
Z. Angew. Math. Phys.
 
70
,
98
(
2020
).
https://doi.org/10.1007/s00033-019-1139-6
Google Scholar
Crossref
Search ADS
 
7.
A. F.
 
Leontiev
,
Series of Exponentials
(
Nauka
,
Moscow
,
1976
). [in Russian]
Google Scholar
 
8.
N. I.
 
Muskhelishvili
,
Some Basic Problems of Mathematical Theory of Elasticity
(
Noordhoff
,
Groningen
,
1953
).
Google Scholar
 
This content is only available via PDF.
© 2022 Author(s).
2022
Author(s)
You do not currently have access to this content.