
 JEAN BAPTISTE JOSEPH F...  Online Information article about JEAN BAPTISTE JOSEPH F... 
  It is known that the sum of an infinite series of continuous terms can be discontinuous only at points in the neighbourhood of which the convergence of the series is not uniform, but nonuniformity of convergence of the series does not necessarily imply discontinuity in the sum. 
  Examples of Fourier's Series.—(a) Let f(x) be given from o to 1, by Ax) =c, when olx<21, and by f(x)c from 21 to 1; it is required to find a sine series, and also a cosine series, which shall represent the function in the interval. 
  The Ultimate Values of the Coefficients in Fourier's Series.—If f(x) is everywhere finite within the given int¢'eval 2r to +vr, it can be shown that an, b,,, the coefficients of cos nx, sin nx in the series which represent the function, are such that na,,, nb,,, however. 
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