Algebra; An Elementary Text book for the Higher Classes of Secondary Schools And for Colleges
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In our eReader you can find the full English version of the book. Read Algebra; An Elementary Text book for the Higher Classes of Secondary Schools And for Colleges Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Algebra; An Elementary Text book for the Higher Classes of Secondary Schools And for Colleges
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In other cases where mod2;=l, the theorem is not in question, owing to the non-convergency of ^JS^z^, In all cases where mod2;> 1, the series S^Cn^ is divergent, and the validity of the theorem is of course out of the question.
EXPONENTIAL AND LOGARITHMIC SERIES — GENERALISATION OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
§*18.] The series l+;? + ^/2! + ^'/3! + . . .
is absolutely convergent for all complex values of z having a finite modulus (see chap, xxvi., § 10). Hence it defines a single...- valued continuous function of z for all values of z. We may call this function the Exponential of z, or shortly Exp;?;* so that Exp^r is defined by the equation Exp;?=l+;? + ;g'/2!+2'/3!+ . . . (1).
The reasoning of chap, xxviii., § 5, presupposes nothing but the absolute convergence of the Exponential Series, and is therefore applicable when the variable is complex. We have therefore the following addition theorem for the function Expz: — * AVhen it is necessary to distinguish between the general function of a complex variable z and the ordinary exponential function of a real variable x, we shall use Exp (with a capital letter) for the former, and either «* or exp x for the latter.
What to read after Algebra; An Elementary Text book for the Higher Classes of Secondary Schools And for Colleges?
You can find similar books in the "Read Also" column, or choose other free books by G George Chrystal to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In other cases where mod2;=l, the theorem is not in question, owing to the non-convergency of ^JS^z^, In all cases where mod2;> 1, the series S^Cn^ is divergent, and the validity of the theorem is of course out of the question.
EXPONENTIAL AND LOGARITHMIC SERIES — GENERALISATION OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
§*18.] The series l+;? + ^/2! + ^'/3! + . . .
is absolutely convergent for all complex values of z having a finite modulus (see chap, xxvi., § 10). Hence it defines a single...- valued continuous function of z for all values of z. We may call this function the Exponential of z, or shortly Exp;?;* so that Exp^r is defined by the equation Exp;?=l+;? + ;g'/2!+2'/3!+ . . . (1).
The reasoning of chap, xxviii., § 5, presupposes nothing but the absolute convergence of the Exponential Series, and is therefore applicable when the variable is complex. We have therefore the following addition theorem for the function Expz: — * AVhen it is necessary to distinguish between the general function of a complex variable z and the ordinary exponential function of a real variable x, we shall use Exp (with a capital letter) for the former, and either «* or exp x for the latter.
What to read after Algebra; An Elementary Text book for the Higher Classes of Secondary Schools And for Colleges?
You can find similar books in the "Read Also" column, or choose other free books by G George Chrystal to read onlineMoreLess
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