Aestu wrote:
Cool. You ever apply for a job working with electronics, civil engineering, nuclear science or lasers, you go ahead and tell them, "I'm not into all that math and textbook stuff, I'm more into METAphysics".
Because, you know, those things totally work because of "tacit knowledge" and not "crammed expressions about physical phenomena" like light, particles, electricity and gravity.
Math can be looked up. Problem?
My post was about learning the methodology and gaining an understanding so that you know how to theorize new phenomenae/particles and/or know how to look for them in raw data.
edit: that, and knowing 'how to math' is more than plugging numbers into equations.
Memorize this:
Code:
\begin{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag A
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_a &=&
T_R C_F\frac{-\pi}{\sin((1+\ep/2)\pi)}
\exp\Bigl(\sum_{i=2}^{\infty}\frac{\zeta_i}{i}\ep^i\Bigr)
\frac{\Gamma(N-\ep/2)\Gamma(N)}
{\Gamma(N+2+\ep/2)\Gamma(N+3-\ep)}
\frac{B(N,3)}{\ep(\ep+2)} \N\\
&& \Bigl(
16N(N+1)^2(N+2)^2 \N\\
&& +8(N+1)(N+2)(3N^3-N^2-6N-4)\ep \N\\
&& +4N(9N^4+12N^3-9N^2-28N-20)\ep^2 \N\\
&& +(10N^5+8N^4+6N^3+24N^2+72N+64)\ep^3 \N\\
&& +(2N^5-10N^4-36N^3-24N^2+24N+16)\ep^4 \N\\
&& +(-4N^4-4N^3+2N^2+2N-12)\ep^5 \N\\
&& +(2N^3+4N^2+2N-4)\ep^6
\Bigr) \N\\
&=&
T_RC_F\Biggl\{
\frac{1}{\ep^{2}}\frac{16}{{N}^{2}(N+1)}
%%%
+\frac{8}{\ep}\frac{2N^3-N-2}{N^3(N+1)^2(N+2)}
%%%
+\frac{8}{{N}^{2}(N+1)}S_2(N)
%
\N\\
%
&&+\frac{4}{N^2(N+1)}\zeta_2
+\frac{4P_1(N)}
{N^4(N+1)^3(N+2)^2}
\Biggr\} + O(\varepsilon)~, \label{resA} \\
%
P_{1}(N)&=&7N^6+18N^5+18N^4-3N^3-21N^2-16N-4~. \N\\ \N
%
%\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag B
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_b &=&T_RC_F\Biggl\{
\frac{1}{\ep^2}\Biggl[
-\frac{32}{N}S_1(N)
+\frac{32}{N}
\Biggr]
%%%%%
+\frac{1}{\ep}\Biggl[
\frac{24S_2(N)-8S^2_1(N)}
{N}
%
\N\\
%
&& +16\frac{N^2+7N+2}
{N(N+1)(N+2)}S_1(N)
-32\frac{N^2+5N+2}
{N(N+1)(N+2)}
\Biggr]
%%%%%
-\frac{16}{N}S_{2,1}(N)
+\frac{40}{3N}S_3(N)
%
\N\\
%
&&-\frac{4}{N}S_1(N)S_2(N)
-\frac{4}{3N}S^3_1(N)
-\frac{8}{N}S_1(N)\zeta_2
+4\frac{
N^2
+7N
+2}
{N(N+1)(N+2)}S^2_1(N)
%
\N\\
%
&&+4\frac{
N^2
-9N
+2}
{N(N+1)(N+2)}S_2(N)
+\frac{8}{N}\zeta_2
-16\frac{N^3+9N^2+8N+4}
{N^2(N+2)^2}S_1(N)
%
\N
\\
%
&&+32\frac{N^5+10N^4+30N^3+37N^2+18N+4}
{N(N+1)^3(N+2)^2}
\Biggl\}~. \label{resB} \\ \N
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag C
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_c&=&T_RC_F\Biggr\{
-\frac{1}{\ep^2}\frac{8}{N}
%%%
+\frac{1}{\ep}\frac{4(13N^4+82N^3+82N^2+N-6)}{N^2(N+1)(N+2)(N+3)}
%%%
+\frac{20}{N}S_2(N)
-\frac{2}{N}\zeta_2
%
\N
\\
%
&&-\frac{2P_2(N)}
{N^3(N+1)^2(N+2)^2(N+3)}
\Biggl\}~, \label{resC}
%\\
\end{eqnarray} \begin{eqnarray}
%
P_2(N)&=&16N^7+176N^6+520N^5+600N^4+257N^3+7N^2+16N+12~. \N\\ \N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag D
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_d&=&T_RC_F\Biggr\{
-\frac{1}{\ep^2}\frac{16}{N}
%%%
+\frac{1}{\ep}\Biggl[
-\frac{8}{N}S_1(N)
+8\frac{
N^3
+10N^2
+59N
+42}
{N(N+1)(N+2)(N+3)}
\Biggr]
%%%
-\frac{2}{N}\Bigl[S_2(N)+S^2_1(N)\Bigr]
%
\N\\
%
&&-\frac{4}{N}\zeta_2
+4\frac{N^4+8N^3+43N^2+36N+12}
{N^2(N+1)^2(N+2)}S_1(N) \N
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\end{eqnarray}
%\newpage
%\begin{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&&-\frac{8P_3(N)}{N(N+1)^3(N+2)^2(N+3)}
\Biggl\}~, \label{resD} \\
%
P_3(N)&=&N^6+10N^5+99N^4+350N^3+486N^2+274N+60~. \N\\ \N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag E
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_e&=&T_R\Biggl[C_F-\frac{C_A}{2}\Biggr] \Biggl\{
\frac{1}{\ep^2}\frac{16(N+3)}{(N+1)^2}
%%%
+\frac{1}{\ep}\Biggl[
-\frac{8(N+2)}{N(N+1)}S_1(N) \N\\
&&-8\frac{
3N^3
+9N^2
+12N
+4}
{N(N+1)^3(N+2)}
\Biggr]
%%
-2\frac{9N^4+40N^3+71N^2-12N-36}
{N(N+1)^2(N+2)(N+3)}S_2(N) \N\\
&&-2\frac{N^3-N^2-8N-36}
{N(N+1)(N+2)(N+3)}S^2_1(N)
+4\frac{(N+3)}{(N+1)^2}\zeta_2 \N\\
%%
&&+4\frac{4N^5+19N^4+31N^3-30N^2-44N-24}
{N^2(N+1)^2(N+2)(N+3)}S_1(N)\N\\
&&+\frac{4P_4(N)}
{N^2(N+1)^4(N+2)^2(N+3)} \Biggr\}~, \label{resE} \\
%
P_4(N)&=&16N^7+111N^6+342N^5+561N^4+536N^3+354N^2+152N+24~. \N \\\N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag F
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_f&=&T_R\Biggl[C_F-\frac{C_A}{2}\Biggr]\Biggl\{
\frac{1}{\ep^2}\Biggl[
\frac{64}{(N+1)(N+2)}S_1(N)
-\frac{64}{(N+1)(N+2)}
\Biggr] \N\\
%%%%%%%%%%%%%%
&& +\frac{1}{\ep}\Biggl[
-\frac{16}{N}S_2(N)
+16\frac{5N+2}
{N^2(N+1)(N+2)}S_1(N)
-\frac{32}{(N+1)^2(N+2)}
\Biggr] \N\\
%%%%%%%%%%%%%%
&& +\frac{16}{N}S_{2,1}(N)
%%%
-\frac{8}{N}S_3(N)
+\frac{16}{(N+1)(N+2)}S_1(N)\zeta_2 \N\\
&& +4\frac{(9N+2)(2N-3)}
{N^2(N+1)(N+2)}S_2(N)
+4\frac{2N^2-3N+2}
{N^2(N+1)(N+2)}S^2_1(N)\N\\
&& -\frac{16}{(N+1)(N+2)}\zeta_2
-8\frac{17N^2+32N+12}
{N(N+1)^2(N+2)^2}S_1(N) \N\\
&& +16\frac{2N^3+12N^2+23N+18}
{(N+1)^3(N+2)^2}
%%%%%%%%%%%%%%%
\Biggr\}~.
\label{resF} \\\N\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag G
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_g&=&T_RC_F\Biggl\{
\frac{1}{\ep^2}\frac{32}{(N+1)(N+2)}
%%%
+\frac{1}{\ep}\Biggl[
\frac{8}{(N+1)(N+2)}S_1(N) \N\\
&&-8\frac{
17N^2
+47N
+28}
{(N+1)^2(N+2)^2}
\Biggr]
%%%
%
%
-\frac{38}
{(N+1)(N+2)}S_2(N)
+\frac{2}{(N+1)(N+2)}S^2_1(N) \N%\\
\end{eqnarray}\begin{eqnarray}
&&+\frac{8}
{(N+1)(N+2)}\zeta_2
-4\frac{3N^3+31N^2+45N+8}
{N(N+1)^2(N+2)^2}S_1(N) \N\\
&&+36\frac{4N^4+26N^3+55N^2+43N+8}
{(N+1)^{3}(N+2)^{3}} \Biggr\}~. \label{resG}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\end{eqnarray}
%\newpage
%\begin{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag H
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_h&=&T_R\Biggl[C_F-\frac{C_A}{2}\Biggr]\Biggl\{
-\frac{1}{\ep^2}\frac{32}{(N+1)(N+2)}
%%%
+\frac{1}{\ep}\Biggl[
16\frac{N+3}
{N(N+1)(N+2)}S_1(N) \N\\
&& -8\frac{N^2+7N+8}
{(N+1)^2(N+2)^2}
\Biggr]
%%%
-4\frac{N^2-18N+9}
{N(N+1)(N+2)(N+3)}S_2(N)
%
\N\\
%
&&-4\frac{N^2-2N+9}
{N(N+1)(N+2)(N+3)}S^2_1(N)
-\frac{8}{(N+1)(N+2)}\zeta_2
%
\N\\
%
&&+4\frac{3N^4+N^3-27N^2-85N-84}
{N(N+1)^2(N+2)^2(N+3)}S_1(N) \N\\
%
&&-4\frac{(N-1)(14N^4+110N^3+337N^2+463N+240)}
{(N+1)^3(N+2)^{3}(N+3)} \Biggr\}~. \label{resH} \\ \N\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag I
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_i&=&
T_RC_A \Biggl\{
\frac{1}{\ep^2}\Biggl[
\frac{16}{(N+1)(N+2)}S_1(N)
-\frac{16(N+4)}{(N+1)(N+2)^2}
\Biggr]
%%%%%
+\frac{1}{\ep}\Biggl[
\frac{32}{(N+2)}S_{-2}(N) \N\\
%%
&& +\frac{4(4N+3)}{(N+1)(N+2)}S_2(N)
-\frac{4}{(N+1)(N+2)}S^2_1(N) \N\\
&& +8\frac{N^3+9N^2+17N+8}{N(N+1)^2(N+2)^2}S_1(N)
%%
-8\frac{2N^3+8N^2+19N+16}{(N+1)^2(N+2)^3}
\Biggr]
%%%%%%
-\frac{32}{N+2}S_{-2,1}(N) \N\\
&&-\frac{8(2N+1)}{(N+1)(N+2)}S_{2,1}(N)
%%
+\frac{16}{N+2}S_{-3}(N)
+\frac{4(18N+17)}{3(N+1)(N+2)}S_3(N) \N\\
&&+\frac{32}{N+2}S_{-2}(N)S_1(N)
%%
+\frac{2(8N+7)}{(N+1)(N+2)}S_{2}(N)S_1(N)
-\frac{2}{3(N+1)(N+2)}S_1^3(N) \N\\
&&+\frac{4}{(N+1)(N+2)}\zeta_2S_1(N)
%%
-\frac{16(N^2-N-4)}{(N+1)(N+2)^2}S_{-2}(N) \N\\
&&-2\frac{4N^4+N^3-7N^2+7N+8}{N(N+1)^2(N+2)^2}S_2(N)
%%
+2\frac{3N^3+7N^2-3N-8}{N(N+1)^2(N+2)^2}S_1^2(N)\N\\
&& -\frac{4(N+4)}{(N+1)(N+2)^2}\zeta_2
%%
-4\frac{4N^5+36N^4+114N^3+174N^2+137N+48}{N(N+1)^3(N+2)^3}S_1(N)
\N\\
%%
&&+4\frac{8N^5+68N^4+247N^3+449N^2+403N+144}{(N+1)^3(N+2)^4}
\Biggr\}\N\\
%%%%%%%%%
&&+T_RC_F \Biggl\{
\frac{1}{\ep}\Biggl[
-\frac{16}{(N+1)(N+2)}S_2(N)
%%
+\frac{16}{(N+1)(N+2)}S_1^2(N)\N\\
&& -\frac{64}{N(N+2)}S_1(N)
+\frac{128}{(N+1)(N+2)}
\Biggr]
%%%%%%%%%%%%%
-\frac{32}{3(N+1)(N+2)}S_3(N)\N\\
&&+\frac{8}{(N+1)(N+2)}S_2(N)S_1(N)
+\frac{8}{3(N+1)(N+2)}S^3_1(N) \N%\\
\end{eqnarray} \begin{eqnarray}
&&+\frac{8(3N+2)}{N(N+1)(N+2)}S_2(N)
-\frac{8(3N-2)}{N(N+1)(N+2)}S_1^2(N)\N\\
&&+\frac{16(5N^2+9N+6)}{N(N+1)^2(N+2)}S_1(N)
-\frac{192}{(N+1)(N+2)}
\Biggr\}.
\label{resI}
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\end{eqnarray}
%\newpage
%\begin{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag J
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_j &=&
-2 T_R C_A
\exp\Biggl(\sum_{i=2}^{\infty}\frac{\zeta_i}{i}\ep^i\Biggr)
\frac{\Gamma(N-\ep/2)\Gamma(N)}
{\Gamma(N+2+\ep/2)\Gamma(N+3-\ep)}
\frac{B(1-\ep/2,\ep/2)}{\ep(\ep+2)} \N\\
&& \Bigl(
4(N+2)(4N^2+4N-5)
-4(11N^2+9N+9)\ep
-(4N^3-2N^2-27N-2)\ep^2 \N\\
&& +(4N^2+2N+9)\ep^3
-2(2N-1)\ep^4
\Bigr) \N\\
&=&T_RC_A\Biggl\{
-\frac{1}{\ep^2}\frac{8(4N^2+4N-5)}
{N^2(N+1)^2}
+\frac{1}{\ep}\frac{4(4N^5+22N^4+11N^3+13N^2+35N+10)}
{N^3(N+1)^3(N+2)}
%
\N\\
%
&& -4\frac{4N^2+4N-5}{N^2(N+1)^2}S_2(N)
-2\frac{4N^2+4N-5}{N^2(N+1)^2}\zeta_2
-\frac{2P_5(N)}
{N^4(N+1)^4(N+2)^2} \Biggr\} + O(\varepsilon) ~, \label{resJ} \\
%
P_5(N)&=&20N^7+64N^6+120N^5+94N^4-140N^3-253N^2-100N-20~. \N\\\N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag K
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_k&=&
4 T_R C_A \exp\Biggl(\sum_{i=2}^{\infty}\frac{\zeta_i}{i}\ep^i\Biggr)
\frac{\Gamma(N+1-\ep/2)\Gamma(N-1)}
{\Gamma(N+2+\ep/2)\Gamma(N+3-\ep)}
\frac{B(1-\ep/2,\ep/2)}{\ep(\ep+2)}
\Bigl(
2(3N^2-23N-20) \N\\
&& -(7N^2+9N+36)\ep
+2(N^2+4N+1)\ep^2
+(4N+9)\ep^3
+2\ep^4
\Bigr) \N\\
&=&T_RC_A\Biggl\{
\frac{1}{\ep^2}\frac{8(3N^2-23N-20)}
{(N-1)N(N+1)^2(N+2)}
-\frac{1}{\ep}\frac{4(10N^4+7N^3+51N^2+172N+112)}
{(N-1)N(N+1)^3(N+2)^2}
%
\N\\
%
&&+4\frac{3N^2-23N-20}
{(N-1)N(N+1)^2(N+2)}S_2(N)
+2\frac{3N^2-23N-20}
{(N-1)N(N+1)^2(N+2)}\zeta_2 \N\\
%
&&+\frac{2P_6(N)}
{(N-1)N(N+1)^4(N+2)^3} \Biggr\} + O(\varepsilon)~, \label{resK} \\
%
P_6(N)&=&14N^6+56N^5+153N^4+139N^3-414N^2-908N-448~.\N\\\N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag L
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_l&=&T_RC_A\Biggl\{
\frac{1}{\ep^2}\Biggl[
\frac{16}{N}S_1(N)
+8\frac{2N^3+5N^2+4N+2}
{N^2(N+1)^2}
\Biggr]
%%%%%%%%
+\frac{1}{\ep}\Biggl[
\frac{4}{N}S_{2}(N)
+\frac{4}{N}S^2_{1}(N) \N\\
&&-\frac{16}{N(N+1)}S_1(N)
%%%
-4\frac{4N^6+30N^5+55N^4+38N^3+4N^2-10N-4}
{N^3(N+1)^3(N+2)}
\Biggr] \N\\
%%%%%%%%
&& +\frac{8}{N}S_{2,1}(N)
+\frac{4}{3N}S_{3}(N)
+\frac{2}{N}S_2(N)S_{1}(N)
+\frac{2}{3N}S^3_{1}(N)
%%%
+\frac{4}{N}S_1(N)\zeta_2 \N\\
&& -4\frac{2N^3+2N^2-N-2}
{N^2(N+1)^2}S_2(N)
-\frac{4}{N(N+1)}S^2_{1}(N)
%%%
+2\frac{2N^3+5N^2+4N+2}
{N^2(N+1)^2}\zeta_2 \N\\
&& -4\frac{(N+2)(2N+1)}
{N^2(N+1)^2}S_1(N)
+2\frac{P_7(N)}
{N^4(N+1)^4(N+2)}
\Biggr\}~,
\label{resL} %\\
\end{eqnarray}\begin{eqnarray}
%%%%%%%%
P_7(N)&=&8N^8+68N^7+164N^6+171N^5+78N^4+12N^3+14N^2+14N+4~. \N\\\N\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag M
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_m&=&T_RC_A\Biggl\{
\frac{1}{\ep^2}\frac{8(N^2-2N-2)}
{N^2(N+1)^2}
%%%%%%
-\frac{1}{\ep}\frac{4(2N^5+11N^4+12N^3+2N^2+6N+4)}
{N^3(N+1)^3(N+2)}\N\\
%%%%%%
&& +4\frac{N^2-2N-2}{N^2(N+1)^2}S_2(N)
+2\frac{N^2-2N-2}{N^2(N+1)^2}\zeta_2
+\frac{2P_8(N)}
{N^4(N+1)^4(N+2)}
\Biggr\}~,
\label{resM} \\
P_8(N)&=&2N^6+7N^5+12N^4+6N^3-8N^2-10N-4~.\N \\\N\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag N
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_n&=&T_RC_A\Biggl\{
\frac{1}{\ep^2}\Biggl[
8\frac{2N^2+3N+2}
{N(N+1)(N+2)}S_1(N)
-8\frac{N(N+3)}
{(N+1)^2(N+2)}
\Biggr] \N\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&&+\frac{1}{\ep}\Biggl[
-16\frac{N-1}
{N(N+1)}S_{-2}(N)
-2\frac{10N^2+21N+6}
{N(N+1)(N+2)}S_2(N)\N\\
&& +2\frac{2N^2+3N+2}
{N(N+1)(N+2)}S^2_1(N)
-4\frac{N^5+6N^4+4N^3-30N^2-40N-8}
{N^2(N+1)^2(N+2)^2}S_1(N) \N
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \end{eqnarray}
% \newpage
% \begin{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&& +4\frac{2N^4+11N^3+15N^2+12N+8}
{(N+1)^3(N+2)^2}
\Biggr]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+16\frac{N-1}
{N(N+1)}S_{-2,1}(N) \N\\
&&+4\frac{4N^2+5N-2}
{N(N+1)(N+2)}S_{2,1}(N)
-8\frac{N-1}
{N(N+1)}S_{-3}(N)\N\\
&&-2\frac{28N^2+45N-14}
{3N(N+1)(N+2)}S_3(N)
-16\frac{N-1}
{N(N+1)}S_{-2}(N)S_1(N)\N\\
&& -\frac{6N^2+5N-18}
{N(N+1)(N+2)}S_2(N)S_1(N)
+\frac{2N^2+3N+2}
{3N(N+1)(N+2)}S^3_1(N) \N\\
&&+2\frac{2N^2+3N+2}
{N(N+1)(N+2)}\zeta_2S_1(N)
+16\frac{N^2-N-4}
{(N+1)^2(N+2)}S_{-2}(N) \N\\
&&+\frac{7N^5+26N^4+16N^3-58N^2-88N-24}
{N^2(N+1)^2(N+2)^2}S_2(N)\N\\
&&-\frac{N^5+6N^4+4N^3-30N^2-40N-8}
{N^2(N+1)^2(N+2)^2}S^2_1(N)
-2\frac{N(N+3)}
{(N+1)^2(N+2)}\zeta_2 \N\\
&&+2\frac{P_9(N)}
{N(N+1)^3(N+2)^3}S_1(N)
-2\frac{P_{10}(N)}
{(N+1)^4(N+2)^3}
\Biggr\}
\label{resN}~, \\
%
P_9(N)&=&2N^6+20N^5+40N^4-45N^3-170N^2-100N+8 ~,
\N\\
%
P_{10}(N)&=&4N^6+32N^5+91N^4+123N^3+62N^2-32N-40~.
\N\\\N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag O
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_o&=&T_RC_A\Biggl\{
%%%
\frac{1}{\ep^2}\Biggl[
-\frac{16}{N(N+2)}S_1(N)
-8\frac{N^2+7N+8}
{(N+1)^2(N+2)^2}
\Biggr]\N\\
%%%
&&+\frac{1}{\ep}\Biggl[
-\frac{4}{N(N+2)}S_2(N)
-\frac{4}{N(N+2)}S_1^2(N)
+4\frac{2N^2+9N+12}
{N(N+1)(N+2)^2}S_1(N) \N\\
&& +4\frac{(11N^3+56N^2+92N+49)N}
{(N+1)^3(N+2)^3}
\Biggr]
%%%
-\frac{8}{N(N+2)}S_{2,1}(N)\N%\\
\end{eqnarray}\begin{eqnarray}
&&-\frac{4}{3N(N+2)}S_3(N)
-\frac{2}{N(N+2)}S_2(N)S_1(N)
-\frac{2}{3N(N+2)}S_1^3(N)\N\\
&&-\frac{4}{N(N+2)}S_1(N)\zeta_2
+\frac{10N^3+31N^2+41N+28}
{N(N+1)^2(N+2)^2}S_2(N) \N\\
&&+\frac{2N^2+9N+12}
{N(N+1)(N+2)^2}S_1^2(N)
-2\frac{N^2+7N+8}
{(N+1)^2(N+2)^2}\zeta_2\N\\
&&+2\frac{4N^4+16N^3-4N^2-61N-48}
{N(N+1)^2(N+2)^3}S_1(N)
-2\frac{P_{11}(N)}
{(N+1)^4(N+2)^4}
%
\Biggr\}~, \label{resO} \\
%
P_{11}(N)&=&28N^6+222N^5+684N^4+1038N^3+811N^2+321N+64~. \N\\\N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag P
% factor 1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_p&=&T_RC_A \Biggr\{
%
\frac{1}{\ep^2}\Biggl[
-8\frac{(N-4)}
{N(N+1)(N+2)}S_1(N)
-8\frac{N+4}
{(N+1)(N+2)^2}
\Biggr] \N\\
%%%
&&+\frac{1}{\ep}\Biggl[
2\frac{3N+4}
{N(N+1)(N+2)}S_2(N)
-2\frac{N-4}
{N(N+1)(N+2)}S^2_1(N) \N
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \end{eqnarray}
% \newpage
% \begin{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&&+4\frac{N^3-17N^2-41N-16}
{N(N+1)^2(N+2)^2}S_1(N)
+4\frac{4N^3+26N^2+51N+32}
{(N+1)^2(N+2)^3}
\Biggr]
%
\N\\
%
%%%
&&-4\frac{N-4}
{N(N+1)(N+2)}S_{2,1}(N)
+\frac{2}{3}\frac{5N+4}
{N(N+1)(N+2)}S_3(N) \N\\
&&-\frac{1}{3}\frac{N-4}
{N(N+1)(N+2)}S^3_1(N)
-\frac{N-4}
{N(N+1)(N+2)}S_1(N)S_2(N) \N\\
&& -2\frac{N-4}
{N(N+1)(N+2)}S_1(N)\zeta_2
-\frac{7N^3+17N^2+13N+16}
{N(N+1)^2(N+2)^2}S_2(N) \N\\
&&+\frac{N^3-17N^2-41N-16}
{N(N+1)^{2}(N+2)^{2}}S^2_1(N)
-2\frac{N+4}
{(N+1)(N+2)^2}\zeta_2 \N\\
&& +2\frac{2N^5+48N^4+174N^3+242N^2+161N+64}
{N(N+1)^3(N+2)^3}S_1(N) \N\\
&&-2\frac{10N^5+92N^4+329N^3+581N^2+507N+176}
{(N+1)^3(N+2)^4} \Biggl\}~. \label{resP}\\ \N\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag Q,R,R'
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_q&=& A^{Qg}_r = A^{Qg}_{r'} = 0
\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag S
% factor -1/2 compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_s&=&T_RC_A\Biggl\{
-\frac{1}{\ep^2}\frac{8}{N^2(N+1)^2}
%%%
+\frac{1}{\ep}\frac{4(2N^3+N^2-3N-1)}
{N^3(N+1)^3}
%%%
-\frac{4}{N^2(N+1)^2}S_2(N)\N\\
&&-\frac{2}{N^2(N+1)^2} \zeta_2
%
-\frac{2P_{12}(N)}
{N^4(N+1)^4(N+2)}\Biggr\}~, \label{resS} \\
%
P_{12}(N)&=&4N^6+4N^5-8N^4-2N^3+16N^2+9N+2~. \N\\
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Diag T
% factor - compared with maple
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A^{Qg}_t&=&T_RC_A\Biggl\{
%
\frac{1}{\ep^2}\frac{8(N^2+3N+4)}
{(N-1)N(N+1)^2(N+2)}
%
-\frac{1}{\ep}\frac{4(2N^4+5N^3-3N^2-20N-16)}
{(N-1)N(N+1)^3(N+2)^2} \N\\
%
&&+4\frac{N^2+3N+4}
{(N-1)N(N+1)^2(N+2)}S_2(N)
%
+2\frac{N^2+3N+4}
{(N-1)N(N+1)^2(N+2)}\zeta_2 \N%\\
\end{eqnarray}\begin{eqnarray}
%
&&+\frac{2P_{13}(N)}{(N-1)N(N+1)^4(N+2)^3}
%
\Biggr\}~, \label{resT} \\
%
P_{13}(N)&=&2N^6+4N^5-13N^4-35N^3+14N^2+92N+64~. \N
%
\end{eqnarray}
Can I get an 'I was wrong'? It's okay, everyone is wrong very often.
edit: I appear to have been wrong, I have this one memorized:
Code:
\Delta p \Delta x \ge\frac{\hbar}{2}