| Isaac Todhunter - 1858 - 530 páginas
...whatever may be the value of x, then by bringing the terras all to one side, we infer that that is, the coefficients of like powers of x in the two series are equal. The theorem here given is sometimes quoted as the Principle of Indeterminate Coefficients; we assumed its... | |
| Isaac Todhunter - 1879 - 856 páginas
......... are always equal whatever may be the value of x, then ^-A0+(a1-Al)x+(a1-As)xt+ ...... that is, the coefficients of like powers of x in the two series are equal. The theorem here given is sometimes quoted as the Principle of Indeterminate Coefficients; we assumed its... | |
| Charles Ambrose Van Velzer, Charles Sumner Slichter - 1888 - 234 páginas
...convergent these two series approach the SAME limit as the number of terms increases, without limit, then the coefficients of like powers of x in the two series are equal each to each. Since we are dealing with the limit of convergent series as the number of terms increases... | |
| Webster Wells - 1889 - 584 páginas
...series A + Bx + CV4 ----- h- Kx" and A' + B'x + C'x--\ ----- \-K'x", are equal for every value of x, the coefficients of like powers of x in the two series are equal. ALGEBRA. APPLICATION TO THE EXPANSION OF FRACTIONS INTO SERIES. 378. 1. Esp&ud 2-Зaг-x3 1 — 2ж+3ж2... | |
| Webster Wells - 1890 - 560 páginas
...has any value which makes both members convergent, and by the Theorem of Undetermined Coefficients, the coefficients of like powers of x in the two series are equal ; that is, A= 2. B — 2A= 0; whence, B= 2 A = 4. -3; whence, C = 2B-3A-3=-l. -1; whence, D=2C-3B-l=-15.... | |
| George P. Lilley - 1894 - 522 páginas
...+ B'x + C'x2 + D'x3 + • ••, where x has any finite value which makes both series convergent, the coefficients of like powers of x, in the two series, are the same. The above method is called The Theorem of Undetermined Coefficients. Notes: 1. The equation... | |
| 1899 - 676 páginas
...or, f(jc) = <v» - (6, - KJ-r"-1 -f (b, - hb, )j— ' + .. . +R- Aft..,. (11) These expressions being identically equal, the coefficients of like powers of x in the two members must be equal ; therefore, na =/<„,«,= b, /(«„, a, == 62 — /i6, , . . . an = R-hbn_,.... | |
| James Harrington Boyd - 1901 - 818 páginas
...conditions since it is equal to series (5). Since the two expansions of a'+". are identically equal, then the coefficients of like powers of x in the two series are equal, thus (6) Al + 2Af4 + 3A3y* + iAty>+ .... [1669] = ^«• = ^(1 + ^+^«+^+ ....). These series are convergent... | |
| James Harrington Boyd - 1901 - 812 páginas
...A<l+Alx+A^+ .... and B^-lB^-^-BfC1-^- .... are equal for all values of x for which they are convergent, then the coefficients of like powers of x in the two series are separately equal. For the values of ./• for which the two series are always convergent they are finite... | |
| Sir Joseph Burn - 1902 - 276 páginas
...Theorems respectively, \ve shall obtain two convergent infinite series in ascending powers of x. Therefore the coefficients of like powers of x in the two series are equal. Art. (314). It is, therefore, only necessary to obtain the coefficient of xn in the right hand member.... | |
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