The Analyst Volume 5-7

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 edition. Excerpt: ...of L and / are changed to positive. It is a resultant formula of adjustment, equivalent to (1) and (2) used in succession. Let the coefficients of the several terms u in (1) and (2) become those of the powers of z in the two polynomials L4-K-3z +L2z2+L1z+l0i + l1: +!2z+l3z+li, When these two are multiplied together, it will be found that the coefficients of the several powers of z in the product are the same as those of the several terms n in the formula (3). Like results are obtained when formulas other than (1) and (2), that is, containing different numbers of terms, are successively used, and we generalize the fact thus. Let any two component formulas be M'0=0m0+1 w1+2 U2 + +- ."0 +Lt --l+L2 -_2+ +Lm u_m I -'0 = i0U0+ij -i+i2 -2+ + L- W- I ' When the given series is adjusted by these two in succession, no matter which is used first, the result will be the same as that of a single adjustment made by a formula whose coefficients are those of the powers of z in the product of the two polynomials l_m +/_m+1 I+U+, 22+...-Ko "+'l 2"+1+ +4. Z2m, m i_. +L_. + 12+i_.+222+. +i02-+i12"+1+ + LnZ J W In the resultant formula, the coefficient of the term w0 is that one which includes the product L0(0. It may be noticed that the coefficients in the product of the polynomial factors are independent of the particular exponents assigned to z in the two factors, provided that each series of exponents is an arithmetical progression, and that both progressions increase by the same constant difference, We might therefore use instead U--+.... +Lt z-+l0 o-Ki i+.... +4.-, (in L_z-+.... +L_lZ-+ L0z+LlZ+.... +Z z," / W where the indices of z are the same as the sub-indices of I, L and u. It follows...show more

Product details

• Paperback | 128 pages
• 189 x 246 x 7mm | 240g
• Miami Fl, United States
• English
• black & white illustrations
• 1236510593
• 9781236510594