An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp
An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp
Samuel Karp
The book An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp was written by author Samuel Karp Here you can read free online of An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp a good or bad book?
What reading level is An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp book?
To quickly assess the difficulty of the text, read a short excerpt:
), p •' 2 a - p y;P ^(p 4 1) ^ + 0(|), (p = 0, 1, ... ), we consider the function 00 / (3U, ^(. IJV).^A, _^v N ^/ av r(|) 1 \ ni(p * 2^ J Tii(p + ^) ttH'-^H where Y is the logarithitdc derivative of the gamma function. Then in accordance with (3U), (35) TTi(-v) 1 + ^J I U-^av/i(p+ ^)n exp r) In deriving (35) a rearrangement has been undertaken which is permissible in virtte of the separate convergence of the various infjjiite products; the procedure here and in what follows is the same as that ...employed in a similar situation i- -■, We rewrite our expression (35) in the form Tri(-v) (36) V^^) 1 + v^ p^ P(v) exp(a-j^v) where a- is a constant given by the series "^'^?{^-^?)- Because of the asymptotic form of v^ > this series converges; the constant Pi - TT ■^ 1 00 (p + j-)- a ^ p is similarly seen to converge. The function P(v), defined by - 17 - P(v) 00 i( V^ - T-. (p + i)/a) /v IT ^1^ — ^x ^-~- ^ i (p + K-)n i £ — . I + 1 \^ a V j can easily be shown to converge unifonnly as |v| ->oo in the upper half of the v-planej the method is again the saine as that used in [2], and depends on the asymptotic form of the /T^* Then, letting |v| ->ao in the upper half-plane, we get P(v) -^ 1, and (37) lim iav 3 lim ^''^;!;i;^^^' -[¥ 4)] ■ (- ^) ^.
User Reviews: