A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 11
... contain- ing a number of arbitrary coefficients equal to the number of coefficients supposed given in p ( x ) . And the actual values of the former might be determined by expressing both mem- bers of the equation in ascending powers of ...
... contain- ing a number of arbitrary coefficients equal to the number of coefficients supposed given in p ( x ) . And the actual values of the former might be determined by expressing both mem- bers of the equation in ascending powers of ...
Side 33
... contain n constants , whose values those conditions determine . We might therefore assume u = A + Bx + Cx2 ... + Ex " -1 ( 8 ) , and determine A , B , C by the linear system of equations formed by making x = a , B. F. D. b ... n , in ...
... contain n constants , whose values those conditions determine . We might therefore assume u = A + Bx + Cx2 ... + Ex " -1 ( 8 ) , and determine A , B , C by the linear system of equations formed by making x = a , B. F. D. b ... n , in ...
Side 34
... contains n arbitrary coefficients . Making x = a , we have - u1 = A ( a − b ) ( a — c ) ... ( a — n ) ; ua therefore A = Κα - ( a − b ) ( a − c ) ... ( a — n ) * In like manner making x = b , we have Ир ( b - a ) ( b - c ) ... ( b ...
... contains n arbitrary coefficients . Making x = a , we have - u1 = A ( a − b ) ( a — c ) ... ( a — n ) ; ua therefore A = Κα - ( a − b ) ( a − c ) ... ( a — n ) * In like manner making x = b , we have Ир ( b - a ) ( b - c ) ... ( b ...
Side 46
... contain an arbitrary constant , or , to speak more strictly , an arbitrary quantity which does not change when x changes to x + 1 , and which is therefore constant relatively to the kind of change denoted by the symbol A. For let v be a ...
... contain an arbitrary constant , or , to speak more strictly , an arbitrary quantity which does not change when x changes to x + 1 , and which is therefore constant relatively to the kind of change denoted by the symbol A. For let v be a ...
Side 55
... contain - 2 * ( x - 1 ) x ( x + 1 ) " x as a factor . And to be its actual value omitting the constant . 2 * - proves Thus also , since A sin ( x ) , A tan1p ( x ) , & c . , are of the respective forms sin ( x ) , tan1 ( x ) , & c . , y ...
... contain - 2 * ( x - 1 ) x ( x + 1 ) " x as a factor . And to be its actual value omitting the constant . 2 * - proves Thus also , since A sin ( x ) , A tan1p ( x ) , & c . , are of the respective forms sin ( x ) , tan1 ( x ) , & c . , y ...
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A₁ A³u algebraic applying arbitrary constant ascending powers assume ax+b B₁ c₂ Calculus of Finite Cambridge CHARLES KINGSLEY cloth CO.'S PUBLICATIONS complete primitive CONIC SECTIONS convergent Crown 8vo curve deduce denoted determine Differential Calculus differential equation divergent English Notes equation of differences expression Fcap Fellow of St Finite Differences functional equation GEORGE BOOLE given equation Hence independent variable indirect integral John's College limit linear equation M.A. Second Edition MACMILLAN & CO.'S method mixed differences operation ordinates P. G. TAIT particular value periodical function rational and integral reduced result Schools second member Sermons shew singular solution substituting successive values supposed symbol theorem tion TODHUNTER Treatise Trinity College u₁ u₂ unity University of Cambridge Ux+1 Ux+2 v₂ Vx+1 Vx+2 whence Их
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