A New Simple And General Method of Solving Numerical Equations of All Orders

Cover A New Simple And General Method of Solving Numerical Equations of All Orders
A New Simple And General Method of Solving Numerical Equations of All Orders
Thomas Weddle
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) . •. Ajr=(l +r) . Ar A^r={l +r) . Ajj* A„_i»-=(l+r) . A„_, Bir=(l+r) . Br B^r=(l+r) . Bj/- &c. Now Ar, Ajr, A^r \-. I^'> Br, Bjr, B^r g _ ^ ; &c. , which we shall denote by A', A\, A\ A'^ ij B', B'j, B'2 B'jj 2 J ^c. , axe the addends employed in article 3, and it ia plain from the above values that they may be derived from each other by the process in article 4. It is also obvious (article 3) that A^=A + Ar + Ajr +A^_ir =A + A'+A', + A'„_i B„_, =B + Br + B, r +B„_2r =B + B' + B\ + B'„_2 &c. ...Hence instead of employing the process in article 4 we may employ the following : ABC y fi a.
+ A' +B' +C' +. / ^^ + A\ +B\ +C\ +y\ + A'„_3 + A'„_2 + B + B «— 3 B— 2 + C'„_3 Cjj 2 V2 + A'„_, B„-x K 6. We shall now proceed to to develope our method.
Let us represent the given equation by F(a;), and the first of the succeeding transformed equations by F^{x^), the second by F^i^z)^ the third by F3(a;3), &c. ; also the limiting equations of F(x) by F'(x), F"(x), &c.


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