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. 1910 Excerpt: ...integral powers of z--zo-All these series are convergent within circles about Zo We have the development of s in powers of z--z0 by multiplying the When we say "within" we mean within any interval that lies wholly within. See Osgood, loc. cil., p. 77 and p. 285. four series together, the multiplication being possible, ...
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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. 1910 Excerpt: ...integral powers of z--zo-All these series are convergent within circles about Zo We have the development of s in powers of z--z0 by multiplying the When we say "within" we mean within any interval that lies wholly within. See Osgood, loc. cil., p. 77 and p. 285. four series together, the multiplication being possible, since the series of the moduli of the terms that constitute the four series are convergent. We thus derive the result: We may develop s = /R(z) in positive integral powers of z--Zo, if Zq is different from the four branch-points a, a2, a3, a. The series is uniformly convergent within the circle about Zq as center, which passes through the nearest of the points Oj, o2, 0,3, 04. Art. 110. We may effect within this circle the same development by Taylor's Theorem in the form 1 R'(zo) 2 s0 so We must decide upon a definite sign of s0 = R(z0) and use this sign throughout the development. If at the beginning we decide upon the other sign, then in the series we must write--so instead of so," that is, all the coefficients are given the opposite sign. If the sign of s0 has been chosen and if the development of s has been made, then s is defined through the above series only within the circle already fixed. If we consider a value of z without the circle of convergence, we do not know what value s will take at this point. To be more explicit we may proceed as follows: Let / be a point without the circle and join z' with z0 through any path of finite length which must not pass indefinitely near a branchpoint. Let the circle of convergence about z0 cut this path at . Then at all points of the portion of path z0 the corresponding values of the function are known through the series. Let z be a point on this portion of path which lie...
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Add this copy of Lectures On the Theory of Elliptic Functions; Volume 1 to cart. $24.01, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
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Add this copy of Lectures On the Theory of Elliptic Functions; Volume 1 to cart. $38.97, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
Add this copy of Lectures On the Theory of Elliptic Functions; Volume 1 to cart. $48.64, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
