A relativistic plasma dispersion function

A relativistic plasma dispersion function is defined, and its analytic properties discussed. Using this function, it should prove possible to formulate relativistic plasma linear theory in a particularly simple form for study either analytically or numerically. As an example, the dispersion relation for Langmuir waves in a one-dimensional relativistic plasma is solved and compared against the results of computer simulations. Agreement is good for waves of phase velocity either above or below the speed of light. Two appendices are provided, the first giving several expansions and other representations of the dispersion function, the second discussing numerical methods for its evaluation. Contour plots of the function are included.