A Treatise on the Calculus of Finite DifferencesMacmillan, 1860 - 248 sider |
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Side 33
... satisfied , viz . that for x = a , x = b ... x = n , it shall assume the respective values ua , u ... un , the expression must contain n constants , whose values those conditions determine . We might therefore assume u = A + Bx + Cx2 ...
... satisfied , viz . that for x = a , x = b ... x = n , it shall assume the respective values ua , u ... un , the expression must contain n constants , whose values those conditions determine . We might therefore assume u = A + Bx + Cx2 ...
Side 55
... satisfied . The result is Σ tani q2 — r2 = 4 ( pr − 1 ) - 2 = C + tan1 . ( 11 ) . r− q − 2rx 1 p + qx + rx2 ( Herschel's Examples , p . 58. ) The above observations may be generalized . The operation denoted by A does not change or ...
... satisfied . The result is Σ tani q2 — r2 = 4 ( pr − 1 ) - 2 = C + tan1 . ( 11 ) . r− q − 2rx 1 p + qx + rx2 ( Herschel's Examples , p . 58. ) The above observations may be generalized . The operation denoted by A does not change or ...
Side 62
... satisfied provided Au , in any term is equal to Σu in the preceding term , and this imposes the condition that the constants in " u , be retained with- out change in " u . And as , if this be done , the equation will be satisfied , it ...
... satisfied provided Au , in any term is equal to Σu in the preceding term , and this imposes the condition that the constants in " u , be retained with- out change in " u . And as , if this be done , the equation will be satisfied , it ...
Side 116
... satisfied . For , on separating the symbols , ( 7 ) becomes = - { D2 + ( b x − αx + 1 ) D — axbx } vx = 0 . Now this may be reduced to the form ( D + bx ) ( D − ax ) vx = 0 , which , lastly , may be resolved into the two 116 [ CH ...
... satisfied . For , on separating the symbols , ( 7 ) becomes = - { D2 + ( b x − αx + 1 ) D — axbx } vx = 0 . Now this may be reduced to the form ( D + bx ) ( D − ax ) vx = 0 , which , lastly , may be resolved into the two 116 [ CH ...
Side 119
... satisfy it were the second member 0 . Let v be such a value , so that vx Vx + n + AxVx + n − 1 + Bx2 + n - 2 + & c . = 0 ............ ( 2 ) , and let u vat ; then ( 1 ) becomes Or = Vx + x ++ AxVx + x + _ + BxVx + -2x + 2 + & c . = X ...
... satisfy it were the second member 0 . Let v be such a value , so that vx Vx + n + AxVx + n − 1 + Bx2 + n - 2 + & c . = 0 ............ ( 2 ) , and let u vat ; then ( 1 ) becomes Or = Vx + x ++ AxVx + x + _ + BxVx + -2x + 2 + & c . = X ...
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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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