. The Bell System technical journal . Tchebycheff polynomials from other viewpoints, seeCourant and Hilbert^, and also a paper by Lanczos on trigonometric interpola-tion. 616 THE BELL SYSTEM TECHXICAL JOURXAL, JULY 1952 Actually, the definitions must \ary ^vith the nature of the useful fre-quency iuter\al. For the present, however, it will be assumed that theuseful interval extends from co = 0 to coc ; or more precisely, fromCO = — Wc to +Wc (in accordance with the symmetries of gain and phasefunctions). Useful intervals which do not include w = 0 require changesin the definitions, which will

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. The Bell System technical journal . Tchebycheff polynomials from other viewpoints, seeCourant and Hilbert^, and also a paper by Lanczos on trigonometric interpola-tion. 616 THE BELL SYSTEM TECHXICAL JOURXAL, JULY 1952 Actually, the definitions must \ary ^vith the nature of the useful fre-quency iuter\al. For the present, however, it will be assumed that theuseful interval extends from co = 0 to coc ; or more precisely, fromCO = — Wc to +Wc (in accordance with the symmetries of gain and phasefunctions). Useful intervals which do not include w = 0 require changesin the definitions, which will be taken up in Section 28. For our present purposes, Tchebycheff polynomials Tk may be definedas follows: p = ico = ioic sin <^Tk = cos /:(/), /: evenTk = i sin k^ ^ ] -(^c\ ^^.^ -1 J {.

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