Functions of a Complex Variable
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FIG. 83.
FIG. 84.
THEOREM II. // the power series Za n z n converges for z = ZQ, it converges absolutely for all values of z for which \z\ | Zi | .
By hypothesis the given series Sa n z n is divergent for z = z\. It must then be divergent for all values of z where | z \ > | Zi | ; for, if ART. 47. ] POWER SERIES 229 it is convergent for any such value of z, say 22, where | 22 | > | z\ |, then it must, by Theorem II, be convergent for all values of z whose modulus is less than [z%\ and therefor...e for z Zi, which is a contra- diction of the given hypothesis.
What to read after Functions of a Complex Variable?
You can find similar books in the "Read Also" column, or choose other free books by E J Edgar Jerome Townsend to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
FIG. 83.
FIG. 84.
THEOREM II. // the power series Za n z n converges for z = ZQ, it converges absolutely for all values of z for which \z\ | Zi | .
By hypothesis the given series Sa n z n is divergent for z = z\. It must then be divergent for all values of z where | z \ > | Zi | ; for, if ART. 47. ] POWER SERIES 229 it is convergent for any such value of z, say 22, where | 22 | > | z\ |, then it must, by Theorem II, be convergent for all values of z whose modulus is less than [z%\ and therefor...e for z Zi, which is a contra- diction of the given hypothesis.
What to read after Functions of a Complex Variable?
You can find similar books in the "Read Also" column, or choose other free books by E J Edgar Jerome Townsend to read onlineMoreLess
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