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If a function with a jump discontinuity is approximated in the norm of L2[ -1, 1] by a periodic spline of order k with equidistant knots, a behavior • . \ analogous to the Glbbs-Wllbraham phenomenon for Fourier series occurs. A set of cardinal splines which play the role of the sine integral function of the classical phenomenon is introduced. It is then shown that as k becomes large, the phenomenon for splines approaches the classical phenomenon.