On the Number of Linearly Independent Solutions of the Riemann Boundary Value Problem on the Riemann Surface of an Algebraic Function

2021 ◽  
Vol 65 (10) ◽  
pp. 10-30
Author(s):  
V. E. Kruglov
Keyword(s):  
Riemann Surface ◽  
Boundary Value Problem ◽  
Algebraic Function ◽  
Boundary Value ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Linearly Independent

The use of Riemann problems in solving a class of transcendental equations

1973 ◽  
Vol 73 (1) ◽  
pp. 111-118 ◽  
Author(s):  
E. E. Burniston ◽  
C. E. Siewert
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Boundary Value ◽  
Explicit Solutions ◽  
Riemann Boundary Value Problem ◽  
Riemann Problems ◽  
Riemann Boundary ◽  
Canonical Solution ◽  
Transcendental Equations ◽  
Explicit Expressions

AbstractA method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed. In particular it is shown by determining a canonical solution of an associated Riemann boundary-value problem that expressions for the roots may be derived in closed form. The explicit solutions to two transcendental equations, tan β = ωβ and β tan β = ω, are discussed in detail, and additional specific results are given.

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