An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp
An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp
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In our eReader you can find the full English version of the book. Read An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp
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), 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)] ■ (- ^) ^.
What to read after An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Karp to read onlineMoreLess
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)] ■ (- ^) ^.
What to read after An Application of Sturm Liouville Theory to a Span Classsearchtermclasssp?
You can find similar books in the "Read Also" column, or choose other free books by Samuel Karp to read onlineMoreLess
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