Asymptotic Expansion of Multiple Integrals And the Method of Stationary Phase
Asymptotic Expansion of Multiple Integrals And the Method of Stationary Phase
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In our eReader you can find the full English version of the book. Read Asymptotic Expansion of Multiple Integrals And the Method of Stationary Phase 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 Asymptotic Expansion of Multiple Integrals And the Method of Stationary Phase
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By integration, d2-l(F, d2. T)"-l/2 2^_^ ^in, n " 2in + 2n " SSTST ^^m, n-l f°r n > 1, derivatives of all orders. Hence it may be neglected because it will not con- tribute to the asymptotic expansion of J, Continuing the integration we obtain I - (-l)"(2n-l)(2n-3)... 1 ^ ^ m, n ( km+i;n; ( 2m+i;n-i! ) . . . ( 2mV^ ) ^ \, o * Further, m, o ^20 20 "'"■'■ >0 — Once again the first term may be neglected insofar as contribution to the asympto- tic expansion is concerned, so that T - (2'"-l)(^-3)...... L /* T ■Sn, c 2m(5m-2)... 2 m "^0, 0 Since „ -, 2 1, d > (d^ - T/F, )^-^^ ^0, 0 " ^17^ ^°s -[TTiTr— 17?
F20 1^1 ^20 and since the numerator in the logarithmic factor will not contribute to the asymptotic expansion, the significant part of I^ ^ is given by 27 - (m-fn)l?nF2j Therefore the relevant part of h^Ct-F^^, ) i£ U Y" ::!_ ^ ^" (-1)'' r-m- r-r-w (t-F^^) ?To at'" tMD Il^b ^^02^"^02^^ v-..^, .^-.. 20 p-0 q'=0 Since we can ignore continuous functions with continuous derivatives we can replace ^ (t-F, )^*^loglt-F, | by if p + q - i.
What to read after Asymptotic Expansion of Multiple Integrals And the Method of Stationary Phase?
You can find similar books in the "Read Also" column, or choose other free books by Douglas S Jones to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
By integration, d2-l(F, d2. T)"-l/2 2^_^ ^in, n " 2in + 2n " SSTST ^^m, n-l f°r n > 1, derivatives of all orders. Hence it may be neglected because it will not con- tribute to the asymptotic expansion of J, Continuing the integration we obtain I - (-l)"(2n-l)(2n-3)... 1 ^ ^ m, n ( km+i;n; ( 2m+i;n-i! ) . . . ( 2mV^ ) ^ \, o * Further, m, o ^20 20 "'"■'■ >0 — Once again the first term may be neglected insofar as contribution to the asympto- tic expansion is concerned, so that T - (2'"-l)(^-3)...... L /* T ■Sn, c 2m(5m-2)... 2 m "^0, 0 Since „ -, 2 1, d > (d^ - T/F, )^-^^ ^0, 0 " ^17^ ^°s -[TTiTr— 17?
F20 1^1 ^20 and since the numerator in the logarithmic factor will not contribute to the asymptotic expansion, the significant part of I^ ^ is given by 27 - (m-fn)l?nF2j Therefore the relevant part of h^Ct-F^^, ) i£ U Y" ::!_ ^ ^" (-1)'' r-m- r-r-w (t-F^^) ?To at'" tMD Il^b ^^02^"^02^^ v-..^, .^-.. 20 p-0 q'=0 Since we can ignore continuous functions with continuous derivatives we can replace ^ (t-F, )^*^loglt-F, | by if p + q - i.
What to read after Asymptotic Expansion of Multiple Integrals And the Method of Stationary Phase?
You can find similar books in the "Read Also" column, or choose other free books by Douglas S Jones to read onlineMoreLess
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