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A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Eds., Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953, p. 162.

has been cited by the following article:

• TITLE: The Khuri-Jones Threshold Factor as an Automorphic Function

  AUTHORS: B. H. Lavenda

  KEYWORDS: Threshold Factor; Automorphic Function; Elliptic and Loxodromic Elements

  JOURNAL NAME: Journal of Modern Physics, Vol.4 No.7, July 8, 2013

  ABSTRACT: The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and ∞ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.