The validity of infinite-series expansion of the form ΣAn cos λnX, of a given function f (X) , is examined. Here, λn (n=1, 2, 3,……) are successive (positive) roots of the equation XsinX + KcosX= 0. The infinite series expansion of the form ΣAn sin μnX, where μn(n=1, 2,……) are successive positive roots of the equation XcosX + KsinX = 0, is well known in connection with the problem of heat-conduction of a spherical body. So that, the author's task was merely to follow the line of thoughts of the older problem. The conclusion quite similar to that of the older problem is arrived at.
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