Algorithm for increasing the accuracy of a numerical solution of the equations of mathematical physics by the Gauss-Legendre method of quadratures

1988 ◽  
Vol 55 (2) ◽  
pp. 930-934
Author(s):  
V. I. Gladkovskii
Keyword(s):  
Numerical Solution ◽  
Mathematical Physics ◽  
Equations Of Mathematical Physics

scholarly journals THE RESIDUE THEOREM AND AN ANALOG OF P. APPELL’S FORMULA FOR FINITE RIEMANN SURFACES

2016 ◽  
pp. 40-45
Author(s):  
Viktor Chueshev ◽  
Viktor Chueshev ◽  
Aleksandr Chueshev ◽  
Aleksandr Chueshev
Keyword(s):  
Riemann Surfaces ◽  
Meromorphic Functions ◽  
Function Theory ◽  
Mathematical Physics ◽  
General Function ◽  
Multiplicative Functions ◽  
Residue Theorem ◽  
Equations Of Mathematical Physics ◽  
Compact Riemann Surfaces ◽  
Integral Order

A theory of multiplicative functions and Prym differentials for the case of special characters on compact Riemann surfaces has found applications in geometrical function theory of complex variable, analytical number theory and in equations of mathematical physics. Theory of functions on compact Riemann surfaces differs from the theory of functions on finite Riemann surfaces even for the class of single meromorphic functions and Abelian differentials. In this article we continue the construction of the general function theory on finite Riemann surfaces for multiplicative meromorphic functions and differentials. We have proved analogues of the theorem on the full sum of residues for Prym differentials of every integral order and P. Appell's formula on expansion of the multiplicative function with poles of arbitrary multiplicity in the sum of elementary Prym integrals.

Partial Differential Equations of Mathematical Physics

Nature ◽  
1932 ◽  
Vol 129 (3267) ◽  
pp. 850-851 ◽  
Author(s):  
E. T. WHITTAKER
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Physics ◽  
Partial Differential ◽  
Equations Of Mathematical Physics
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