 X(px + c0 = 0, or, which is ultimately the same thing, of ex' + c0 = 0 ; the latter of fx = 0. The number of imaginary roots of the infinite group is therefore v or v — 1 according as v is even or odd ; ie, is the same as the number of changes of sign...  Mathematical Questions and Solutions - Page 391869Full view - About this book
 | 1868 - 380 pages
...imaginary roots of the infinite group is therefore v or v — 1 according as v is even or odd ; ie, is the same as the number of changes of sign in the...will not be affected if we multiply each quantity, ««,«!, <*3, ..... °y the common factor MiM + l) ---- (A' + ''-l)> ^ wh;ch is 1 . 2 .... ft the... | |
 | W. J. C. Miller - Mathematics - 1869 - 120 pages
...imaginary roots of the infinite group is therefore v or v— 1 according as v is even or odd ; ie, is the same as the number of changes of sign in the...series. Hence the number of imaginary roots belonging to ff=0 cannot be less than the number of sign-changes in the lower series; but this last number will... | |
 | Adam Ostaszewski - Mathematics - 1990 - 564 pages
...pk(i.) and pk+ ,(A) interlace (see Figure 7.3); (c) the number of zeros of pB(A) which are less than A0 is the same as the number of changes of sign in the sequence: \ Any zero values appearing in this list should be suppressed for the purposes of counting... | |
 | Physics - 1923 - 1264 pages
...values of p* given by (14) are all real, and, also, the number between p2 = a and p3 = /3, where «</8, is the same as the number of changes of sign in the above series which is gained as ;>* increases from « to /9. Firstly, suppose a> below both " whirling... | |
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