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SandBoxExpOfEnd

Edit detail for SandBoxExpOfEnd revision 1 of 18

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Editor: Bill Page Time: 2014/09/11 05:39:22 GMT+0
Note:

changed:
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one
\begin{axiom}
1
eq42 := _
  -r2*r3*r4*exp(r1)/((r1-r2)*(r1-r3)*(r1-r4)) + _
  -r1*r3*r4*exp(r2)/((r2-r1)*(r2-r3)*(r2-r4)) + _
  -r1*r2*r4*exp(r3)/((r3-r1)*(r3-r2)*(r3-r4)) + _
  -r1*r2*r3*exp(r4)/((r4-r1)*(r4-r2)*(r4-r3))
\end{axiom}
three
\begin{axiom}
htrigs eval(eq42, [r3=-r1,r4=-r2])
htrigs limit(%,r2=r1)
\end{axiom}

\begin{axiom}
eq43 :=
  (r2*r3 + r3*r4 + r4*r2)*exp(r1)/((r1-r2)*(r1-r3)*(r1-r4)) + _
  (r1*r3 + r3*r4 + r4*r1)*exp(r2)/((r2-r1)*(r2-r3)*(r2-r4)) + _
  (r1*r2 + r2*r4 + r4*r1)*exp(r3)/((r3-r1)*(r3-r2)*(r3-r4)) + _
  (r1*r2 + r2*r3 + r3*r1)*exp(r4)/((r4-r1)*(r4-r2)*(r4-r3))
\end{axiom}

\begin{axiom}
htrigs eval(eq43, [r3=-r1,r4=-r2])
htrigs limit(%,r2=r1)
\end{axiom}

one

fricas

$\label{eq1}1$

(1)

Type: PositiveInteger?

fricas

eq42 := _
  -r2*r3*r4*exp(r1)/((r1-r2)*(r1-r3)*(r1-r4)) + _
  -r1*r3*r4*exp(r2)/((r2-r1)*(r2-r3)*(r2-r4)) + _
  -r1*r2*r4*exp(r3)/((r3-r1)*(r3-r2)*(r3-r4)) + _
  -r1*r2*r3*exp(r4)/((r4-r1)*(r4-r2)*(r4-r3))

$\label{eq2}{\left( \begin{array}{@{}l} \displaystyle {{\left({ \begin{array}{@{}l} \displaystyle {{\left(-{r 1 \ {{r 2}^{2}}}+{{{r 1}^{2}}\ r 2}\right)}\ {{r 3}^{3}}}+ \ \ \displaystyle {{\left({r 1 \ {{r 2}^{3}}}-{{{r 1}^{3}}\ r 2}\right)}\ {{r 3}^{2}}}+ \ \ \displaystyle {{\left(-{{{r 1}^{2}}\ {{r 2}^{3}}}+{{{r 1}^{3}}\ {{r 2}^{2}}}\right)}\ r 3}$

(2)

Type: Expression(Integer)

three

fricas

htrigs eval(eq42, [r3=-r1,r4=-r2])

$\label{eq3}{-{{{r 1}^{2}}\ {\cosh \left({r 2}\right)}}+{{{r 2}^{2}}\ {\cosh \left({r 1}\right)}}}\over{{{r 2}^{2}}-{{r 1}^{2}}}$

(3)

Type: Expression(Integer)

fricas

htrigs limit(%,r2=r1)

$\label{eq4}{-{r 1 \ {\sinh \left({r 1}\right)}}+{2 \ {\cosh \left({r 1}\right)}}}\over 2$

(4)

Type: Expression(Integer)

fricas

eq43 :=
  (r2*r3 + r3*r4 + r4*r2)*exp(r1)/((r1-r2)*(r1-r3)*(r1-r4)) + _
  (r1*r3 + r3*r4 + r4*r1)*exp(r2)/((r2-r1)*(r2-r3)*(r2-r4)) + _
  (r1*r2 + r2*r4 + r4*r1)*exp(r3)/((r3-r1)*(r3-r2)*(r3-r4)) + _
  (r1*r2 + r2*r3 + r3*r1)*exp(r4)/((r4-r1)*(r4-r2)*(r4-r3))

$\label{eq5}{\left( \begin{array}{@{}l} \displaystyle {{\left({ \begin{array}{@{}l} \displaystyle {{\left({{r 2}^{2}}-{{r 1}^{2}}\right)}\ {{r 3}^{3}}}+{{\left(-{{r 2}^{3}}+{{r 1}^{3}}\right)}\ {{r 3}^{2}}}+ \ \ \displaystyle {{{r 1}^{2}}\ {{r 2}^{3}}}-{{{r 1}^{3}}\ {{r 2}^{2}}}$

(5)

Type: Expression(Integer)

fricas

htrigs eval(eq43, [r3=-r1,r4=-r2])

$\label{eq6}{-{{{r 1}^{3}}\ {\sinh \left({r 2}\right)}}+{{{r 2}^{3}}\ {\sinh \left({r 1}\right)}}}\over{{r 1 \ {{r 2}^{3}}}-{{{r 1}^{3}}\ r 2}}$

(6)

Type: Expression(Integer)

fricas

htrigs limit(%,r2=r1)

$\label{eq7}{{3 \ {\sinh \left({r 1}\right)}}-{r 1 \ {\cosh \left({r 1}\right)}}}\over{2 \ r 1}$

(7)

Type: Expression(Integer)