A Treatise on the Calculus of Finite Differences |
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Page 3
... assuming t = hx we have At hAx , whence Ax = 1 . - Thus it suffices to establish the rules of the calculus on the assumption that the finite difference of the independent variable is unity . At the same time it will be noted that this A ...
... assuming t = hx we have At hAx , whence Ax = 1 . - Thus it suffices to establish the rules of the calculus on the assumption that the finite difference of the independent variable is unity . At the same time it will be noted that this A ...
Page 11
... Assume ( x ) = a + bx + cx ( 2 ) + dx ( 3 ) + hx ( m ) ......... ... ( 1 ) . The legitimacy of this form is evident , for it represents a rational and integral function of x of the nth degree , contain- ing a number of arbitrary ...
... Assume ( x ) = a + bx + cx ( 2 ) + dx ( 3 ) + hx ( m ) ......... ... ( 1 ) . The legitimacy of this form is evident , for it represents a rational and integral function of x of the nth degree , contain- ing a number of arbitrary ...
Page 28
... assumed a priori . It may be that the evident character of succession in the values observed indicates what kind of ... assume for the general expression of the values under consideration a rational and integral function of x , and to ...
... assumed a priori . It may be that the evident character of succession in the values observed indicates what kind of ... assume for the general expression of the values under consideration a rational and integral function of x , and to ...
Page 29
... assumes different forms , according as the values given are equidistant , i . e . corre- spondent to equidifferent ... assuming as the approximate general expression of u u2 = A + Bx + Сx2 ... + Ex " -1 ....... ( 1 ) , a form which is ...
... assumes different forms , according as the values given are equidistant , i . e . corre- spondent to equidifferent ... assuming as the approximate general expression of u u2 = A + Bx + Сx2 ... + Ex " -1 ....... ( 1 ) , a form which is ...
Page 33
... assume this expression rational and integral , Art . 1 . Now there being n conditions to be satisfied , viz . that for x = a , x = b ... x = n , it shall assume the respective values Иая Из un , the expression must contain n constants ...
... assume this expression rational and integral , Art . 1 . Now there being n conditions to be satisfied , viz . that for x = a , x = b ... x = n , it shall assume the respective values Иая Из un , the expression must contain n constants ...
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Common terms and phrases
2ndly Ału algebraic applying arbitrary constant ascending powers assume ax+b B₁ C₁ C₂ Calculus of Finite Cambridge Chap CHARLES KINGSLEY cloth CO.'S PUBLICATIONS complete primitive condition Crown 8vo curve deduce denoted determine develope Differential Calculus differential coefficients differential equation English Notes equation of differences Examples expression Fcap Finite Differences functional equation GEORGE BOOLE given equation Hence independent variable indirect integral limit linear equation M.A. Second Edition MACMILLAN & CO.'S method mixed differences operation ordinates particular value periodical function rational and integral reduced represented result roots second member Sermons shew singular solution substituting successive values supposed symbol theorem tion TODHUNTER Treatise Trinity College u₁ u₂ unity University of Cambridge Ux,y Ux+1 Ux+2 v₂ Vx+1 whence Их
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