A Treatise on the Calculus of Finite Differences |
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Page 3
... reduces to equivalence the symbols and A. Ax We shall therefore in the following chapters develope the theory of the operation denoted by A and defined by the equation Aux = Ux + 1 - Ux · But we shall , where convenience suggests ...
... reduces to equivalence the symbols and A. Ax We shall therefore in the following chapters develope the theory of the operation denoted by A and defined by the equation Aux = Ux + 1 - Ux · But we shall , where convenience suggests ...
Page 12
... reduction , x is to be made equal to 0 . Maclaurin's theorem is the limiting form to which the above theorem approaches when the increment Ax is inde- finitely diminished . General theorems expressing relations between the successive ...
... reduction , x is to be made equal to 0 . Maclaurin's theorem is the limiting form to which the above theorem approaches when the increment Ax is inde- finitely diminished . General theorems expressing relations between the successive ...
Page 30
... a by means of the differences of the powers of 0 . By means of the same differences , find a finite expression for the infinite series 1m.x - 3m . + 5m 3 15 + & c . where m is a positive integer , and reduce the 30 [ EX . 9 . EXERCISES .
... a by means of the differences of the powers of 0 . By means of the same differences , find a finite expression for the infinite series 1m.x - 3m . + 5m 3 15 + & c . where m is a positive integer , and reduce the 30 [ EX . 9 . EXERCISES .
Page 31
George Boole, John Fletcher Moulton. where m is a positive integer , and reduce the result when 15. Prove that m = = 4 . F ( E ) a * px = a * F ( aE ) $ x , ( x △ ) 1u2 = ( x + n − 1 ) Aux , - f ( A ) ( E ) ” = ( E ) ” f ( A + mua and ...
George Boole, John Fletcher Moulton. where m is a positive integer , and reduce the result when 15. Prove that m = = 4 . F ( E ) a * px = a * F ( aE ) $ x , ( x △ ) 1u2 = ( x + n − 1 ) Aux , - f ( A ) ( E ) ” = ( E ) ” f ( A + mua and ...
Page 43
... reduces of course to Lagrange's formula . Application to Statistics . 9. When the results of statistical observations are pre- sented in a tabular form it is sometimes required to narrow the intervals to which they correspond , or to ...
... reduces of course to Lagrange's formula . Application to Statistics . 9. When the results of statistical observations are pre- sented in a tabular form it is sometimes required to narrow the intervals to which they correspond , or to ...
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Algebra applied approximate arbitrary constant Arithmetic assume B₁ Bernoulli's numbers C₁ C₂ Calculus of Finite Cambridge chapter Christ's College cloth College complete primitive convergent Crelle Crown 8vo curve deduce denoted determine difference-equation Differential Calculus differential coefficients differential equation divergent divergent series dy dx English equal Examples expression factor Fcap Finite Differences formula functional equation geometrical given equation gives Grunert Hence independent variable indirect integral integral function Lagrange's formula limits Mathematical method obtain operation ordinates P₁ P₂ particular periodical function problem Professor quantity rational and integral Schlömilch Schools Second Edition second member shew singular solution solve student substituting summation supposed symbol Taylor's Theorem theorem tion u₁ u₂ unity Ux+1 Ux+2 V₁ v₂ Vx+1 whence Их
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