Riemann boundary-value problem with index minus infinity on a rectifiable curve

1990 ◽  
Vol 42 (10) ◽  
pp. 1199-1204 ◽  
Author(s):  
S. A. Plaksa
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Rectifiable Curve

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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