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 Oct 4 awarded Supporter Dec 11 revised Integral $\int_{0}^\infty\frac {(1-{{e}^{-i (q-p)t}})ln(|p^2-p_0^2|)}{(q-p)({{ p}}^{2}-{{p_1}}^{2})({{p}}^{2}-{{p_2} }^{2})}dp$ since the contribution by the imaginary part of the logarithm is solvable, I changed the logarithm's argument to its absolute value. Dec 10 revised Integral $\int_{0}^\infty\frac {(1-{{e}^{-i (q-p)t}})ln(|p^2-p_0^2|)}{(q-p)({{ p}}^{2}-{{p_1}}^{2})({{p}}^{2}-{{p_2} }^{2})}dp$ comment added Dec 10 revised Integral $\int_{0}^\infty\frac {(1-{{e}^{-i (q-p)t}})ln(|p^2-p_0^2|)}{(q-p)({{ p}}^{2}-{{p_1}}^{2})({{p}}^{2}-{{p_2} }^{2})}dp$ added 83 characters in body Dec 10 revised Integral $\int_{0}^\infty\frac {(1-{{e}^{-i (q-p)t}})ln(|p^2-p_0^2|)}{(q-p)({{ p}}^{2}-{{p_1}}^{2})({{p}}^{2}-{{p_2} }^{2})}dp$ deleted 26 characters in body Dec 10 asked Integral $\int_{0}^\infty\frac {(1-{{e}^{-i (q-p)t}})ln(|p^2-p_0^2|)}{(q-p)({{ p}}^{2}-{{p_1}}^{2})({{p}}^{2}-{{p_2} }^{2})}dp$ Dec 10 awarded Tumbleweed Apr 1 comment Align basis of vector space with that of subspace I need a basis of $V$ which contains the given basis of $S$ as subset. Alternatively the basis of $S$ may be transformed into a new basis of $S$ (possibly orthogonal). In this case I need a basis of $V$ which contains the transformed basis of $S$ as subset. Apr 1 comment Align basis of vector space with that of subspace Yes, agreed, it does not meet my question, but in fact an orthogonal basis could have advantages for my application. But, would the the non-zero orthogonal vectors be indeed linearly independent of ${s_i}$, the basis of $S$. In principle I am flexible also to change the basis of S to one which is orthogonal. Apr 1 comment Align basis of vector space with that of subspace Now I see your point. Seemingly my linear algebra is a bit rusty. Mar 31 comment Align basis of vector space with that of subspace Thanks for the fast reply. I think I was not clear enough. $w_i$ were supposed to be elements of the basis of $V$ (those $v_i$ which are not linearly dependent on $s_i$; i.e. $w_i$ are already linearly independent). Our approaches should therefore be equivalent, or not? Mar 31 revised Align basis of vector space with that of subspace corrected grammar Mar 31 asked Align basis of vector space with that of subspace Nov 16 revised Approximation of integral using series expansion of the integrand. typeset equation Nov 15 awarded Editor Nov 15 revised Approximation of integral using series expansion of the integrand. added 31 characters in body Nov 15 awarded Student Nov 15 asked Approximation of integral using series expansion of the integrand.