The Analysis of Contour Integrals
For any 𝑛, the contour integral 𝑦=cosh𝑛+1𝑥∮𝐶(cosh(𝑧𝑠)/(sinh𝑧−sinh𝑥)𝑛+1𝑑𝑧,𝑠2=−𝜆, is associated with differential equation 𝑑2𝑦(𝑥)/𝑑𝑥2+(𝜆+𝑛(𝑛+1)/cosh2𝑥)𝑦(𝑥)=0. Explicit solutions for 𝑛=1 are obtained. For 𝑛=1, eigenvalues, eigenfunctions, spectral function, and eigenfunction expansions are explored....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/765920 |