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Show: Let f and g be elliptic functions for the same lattice. (a) If f and g have the same poles, and for each pole respectively the same principal parts, then f and g differ by an additive constant. (b) If f and g have the same pole set and the same zero set, and if for any pole or zero the corresponding multiplicities coincide, then f and g differ by a multiplicative constant.

Show: Let f and g be elliptic functions for the same lattice. (a) If f and g have the same poles, and for each pole respectively the same principal parts, then f and g differ by an additive constant. (b) If f and g have the same pole set and the same zero set, and if for any pole or zero the corresponding multiplicities coincide, then f and g differ by a multiplicative constant.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show: Let f and g be elliptic functions for the same lattice. (a) If f and g have the same poles, and for each pole respectively the same principal parts, then ƒ and g differ by an additive constant. (b) If f and g have the same pole set and the same zero set, and if for any pole or zero the corresponding multiplicities coincide, then f and g differ by a multiplicative constant.
Transcribed Image Text:Show: Let f and g be elliptic functions for the same lattice. (a) If f and g have the same poles, and for each pole respectively the same principal parts, then ƒ and g differ by an additive constant. (b) If f and g have the same pole set and the same zero set, and if for any pole or zero the corresponding multiplicities coincide, then f and g differ by a multiplicative constant.
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