A Treatise on the Calculus of Finite Differences |
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... APPROXIMATE SUMMATION OF SERIES Development of Zu ,, 8o . Bernoulli's Numbers , 83. Applications , 84 . Limits of the Series for Zu- , 91. Other forms of Zu ,, 94. Exercises , 97 . 45 65 80 PAGE CHAPTER VII . EQUATIONS OF DIFFERENCES ...
... APPROXIMATE SUMMATION OF SERIES Development of Zu ,, 8o . Bernoulli's Numbers , 83. Applications , 84 . Limits of the Series for Zu- , 91. Other forms of Zu ,, 94. Exercises , 97 . 45 65 80 PAGE CHAPTER VII . EQUATIONS OF DIFFERENCES ...
Page 29
... approximate general expression of u u2 = A + Bx + Сx2 ... + Ex " -1 ....... ( 1 ) , a form which is rational and integral and involves n arbitrary coefficients , the data in succession give n - 1 ua = A + Ba + Ca3 ... + Ea " -1 , u2 = A ...
... approximate general expression of u u2 = A + Bx + Сx2 ... + Ex " -1 ....... ( 1 ) , a form which is rational and integral and involves n arbitrary coefficients , the data in succession give n - 1 ua = A + Ba + Ca3 ... + Ea " -1 , u2 = A ...
Page 30
... approximate value of log 3.14159 . Here , omitting the decimal point , we have the following table of numbers and differences : Ио U1 U2 Из 3 4969296 4983106 4996871 5010593 A 13810 A2 -45 13765 - 43 13722 A3 2 The first column gives ...
... approximate value of log 3.14159 . Here , omitting the decimal point , we have the following table of numbers and differences : Ио U1 U2 Из 3 4969296 4983106 4996871 5010593 A 13810 A2 -45 13765 - 43 13722 A3 2 The first column gives ...
Page 32
... 24853 , the true value being 24858 . To shew the gradual closing of the approximation as the number of the values given is increased , the following results are added : Data . W s น.น. ub Uz , u uz 32 [ CH . III . OF INTERPOLATION .
... 24853 , the true value being 24858 . To shew the gradual closing of the approximation as the number of the values given is increased , the following results are added : Data . W s น.น. ub Uz , u uz 32 [ CH . III . OF INTERPOLATION .
Page 33
... approximate general expression for u . We shall 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 ...
... approximate general expression for u . We shall 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 ...
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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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