Three-particle finite-volume formalism for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> and related systems

We consider three-particle systems consisting of two identical particles and a third that is different, with all being spinless. Examples include $\pi^+\pi^+ K^+$ $K^+K^+\pi^+$. derive the formalism necessary to extract two- infinite-volume scattering amplitudes from spectrum such in finite volume. use relativistic based on an all-orders diagrammatic analysis generic effective field theory, adopting methodology used recently study case three nondegenerate particles. present both direct derivation, also cross-check appropriate limit projection fully formalism. work out threshold expansions for K matrix will be needed practical applications, plus third, theory.