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SandBoxDoublePowerSeries

Edit detail for SandBoxDoublePowerSeries revision 7 of 19

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Editor: Bill Page Time: 2014/08/21 01:56:46 GMT+0
Note:

added:
aa(0,l)
aa(k,0)

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a!

$\label{eq1}a !$

(1)

Type: Variable(a!)

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!:=operator '!

$\label{eq2}!$

(2)

Type: BasicOperator?

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a(i,j)==(1+(j-1)*i)/!(2*i+4*j)

Type: Void

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a0:=matrix [[a(i,j)*k^i*l^j for i in 0..5] for j in 1..4]

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Compiling function a with type (NonNegativeInteger,PositiveInteger)
       -> Expression(Integer)

$\label{eq3}\left[ \begin{array}{cccccc} {l \over{! \left({4}\right)}}&{{k \ l}\over{! \left({6}\right)}}&{{{{k}^{2}}\ l}\over{! \left({8}\right)}}&{{{{k}^{3}}\ l}\over{! \left({1 0}\right)}}&{{{{k}^{4}}\ l}\over{! \left({12}\right)}}&{{{{k}^{5}}\ l}\over{! \left({14}\right)}} \ {{{l}^{2}}\over{! \left({8}\right)}}&{{2 \ k \ {{l}^{2}}}\over{! \left({10}\right)}}&{{3 \ {{k}^{2}}\ {{l}^{2}}}\over{! \left({1 2}\right)}}&{{4 \ {{k}^{3}}\ {{l}^{2}}}\over{! \left({14}\right)}}&{{5 \ {{k}^{4}}\ {{l}^{2}}}\over{! \left({16}\right)}}&{{6 \ {{k}^{5}}\ {{l}^{2}}}\over{! \left({18}\right)}} \ {{{l}^{3}}\over{! \left({12}\right)}}&{{3 \ k \ {{l}^{3}}}\over{! \left({14}\right)}}&{{5 \ {{k}^{2}}\ {{l}^{3}}}\over{! \left({1 6}\right)}}&{{7 \ {{k}^{3}}\ {{l}^{3}}}\over{! \left({18}\right)}}&{{9 \ {{k}^{4}}\ {{l}^{3}}}\over{! \left({20}\right)}}&{{{11}\ {{k}^{5}}\ {{l}^{3}}}\over{! \left({22}\right)}} \ {{{l}^{4}}\over{! \left({16}\right)}}&{{4 \ k \ {{l}^{4}}}\over{! \left({18}\right)}}&{{7 \ {{k}^{2}}\ {{l}^{4}}}\over{! \left({2 0}\right)}}&{{{10}\ {{k}^{3}}\ {{l}^{4}}}\over{! \left({22}\right)}}&{{{1 3}\ {{k}^{4}}\ {{l}^{4}}}\over{! \left({24}\right)}}&{{{16}\ {{k}^{5}}\ {{l}^{4}}}\over{! \left({26}\right)}}$

(3)

Type: Matrix(Expression(Integer))

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a(i,j)==(1+(j-1)*i)/Gamma(1+2*i+4*j)

   Compiled code for a has been cleared.
   1 old definition(s) deleted for function or rule a

Type: Void

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aa(k,l)==1+reduce(+,concat [[a(i,j)*k^i*l^j for i in 0..10] for j in 1..11])

Type: Void

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aa(0,l)

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Compiling function a with type (NonNegativeInteger,PositiveInteger)
       -> Expression(Integer)

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Compiling function aa with type (NonNegativeInteger,Variable(l)) -> 
      Expression(Integer)

$\label{eq4}{\left( \begin{array}{@{}l} \displaystyle {{l}^{11}}+{{3258024}\ {{l}^{10}}}+{{7146019520640}\ {{l}^{9}}}+ \ \ \displaystyle {{10102470716719180800}\ {{l}^{8}}}+ \ \ \displaystyle {{8718836327357321797632000}\ {{l}^{7}}}+ \ \ \displaystyle {{4284436171263387931356364800000}\ {{l}^{6}}}+ \ \ \displaystyle {{1092634050140274243806225576755200000}\ {{l}^{5}}}+ \ \ \displaystyle {{127051487350311089069787910065094656000000}\ {{l}^{4}}}+ \ \ \displaystyle {{ \begin{array}{@{}l}\displaystyle 5549608967461588370568335911643334574080000 \ 000$

(4)

Type: Expression(Integer)

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aa(k,0)

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Compiling function aa with type (Variable(k),NonNegativeInteger) -> 
      Expression(Integer)

$\label{eq5}1$

(5)

Type: Expression(Integer)

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aa(1,1)::Float

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Compiling function aa with type (PositiveInteger,PositiveInteger)
       -> Expression(Integer)

$\label{eq6}1.0431059959_804562675$

(6)

Type: Float

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aa(0,0)::Float

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Compiling function aa with type (NonNegativeInteger,
      NonNegativeInteger) -> Expression(Integer)

$\label{eq7}1.0$

(7)

Type: Float

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aa(-1,-1)::Float

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Compiling function aa with type (Integer,Integer) -> Expression(
      Integer)

$\label{eq8}0.9597219487_3670537$

(8)

Type: Float

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i0:=a(1/2+%i*beta,0)*(-x)^(1/2+%i*beta)/cosh(%pi*beta)

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Compiling function a with type (Polynomial(Fraction(Complex(Integer)
      )),NonNegativeInteger) -> Expression(Complex(Integer))

$\label{eq9}{{\left(-{2 \ i \ beta}+ 1 \right)}\ {{\left(- x \right)}^{{{2 \ i \ beta}+ 1}\over 2}}}\over{2 \ {\Gamma \left({{2 \ i \ beta}+ 2}\right)}\ {\cosh \left({beta \ \pi}\right)}}$

(9)

Type: Expression(Complex(Integer))

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i1:=a(0,1/2+%i*delta)*(-y)^(1/2+%i*delta)/cosh(%pi*delta)

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Compiling function a with type (NonNegativeInteger,Polynomial(
      Fraction(Complex(Integer)))) -> Expression(Complex(Integer))

$\label{eq10}{{\left(- y \right)}^{{{2 \ i \ delta}+ 1}\over 2}}\over{{\Gamma \left({{4 \ i \ delta}+ 3}\right)}\ {\cosh \left({delta \ \pi}\right)}}$

(10)

Type: Expression(Complex(Integer))

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i2:=a(1/2+%i*beta,1/2+%i*delta)*(-y)^(1/2+%i*delta)/(cosh(%pi*beta)*cosh(%pi*delta))

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Compiling function a with type (Polynomial(Fraction(Complex(Integer)
      )),Polynomial(Fraction(Complex(Integer)))) -> Expression(Complex(
      Integer))

$\label{eq11}{\left({\left({ \begin{array}{@{}l} \displaystyle {{\left(-{4 \ beta}+{2 \ i}\right)}\ delta}- \ \ \displaystyle {2 \ i \ beta}+ 3$

(11)

Type: Expression(Complex(Integer))

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eval(i0,beta=-1)

$\label{eq12}{{\left(1 +{2 \ i}\right)}\ {{\left(- x \right)}^{{1 -{2 \ i}}\over 2}}}\over{2 \ {\Gamma \left({2 -{2 \ i}}\right)}\ {\cosh \left({\pi}\right)}}$

(12)

Type: Expression(Complex(Integer))

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eval(i0,beta=0)

$\label{eq13}{\sqrt{- x}}\over 2$

(13)

Type: Expression(Complex(Integer))

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eval(i0,beta=1)

$\label{eq14}{{\left(1 -{2 \ i}\right)}\ {{\left(- x \right)}^{{1 +{2 \ i}}\over 2}}}\over{2 \ {\Gamma \left({2 +{2 \ i}}\right)}\ {\cosh \left({\pi}\right)}}$

(14)

Type: Expression(Complex(Integer))

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eval(i0,[beta=1,x=1])

$\label{eq15}{{\left(1 -{2 \ i}\right)}\ {{\left(- 1 \right)}^{{1 +{2 \ i}}\over 2}}}\over{2 \ {\Gamma \left({2 +{2 \ i}}\right)}\ {\cosh \left({\pi}\right)}}$

(15)

Type: Expression(Complex(Integer))

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%::Expression Complex Float

$\label{eq16}{{0.0037279237_7925005573_54}+{{0.0018639618_8962502786_77}\ i}}\over{\Gamma \left({{2.0}+{{2.0}\ i}}\right)}$

(16)

Type: Expression(Complex(Float))

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%::Complex Float

   Cannot convert from type Expression(Complex(Float)) to Complex(Float
      ) for value
   0.0037279237_7925005573_54 + 0.0018639618_8962502786_77 %i
   ----------------------------------------------------------
                       Gamma(2.0 + 2.0 %i)

Gamma(2+%i*2)

$\label{eq17}\Gamma \left({2 +{2 \ i}}\right)$

(17)

Type: Expression(Complex(Integer))

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Gamma(2.0+%i*2.0)

$\label{eq18}\begin{array}{@{}l} \displaystyle {0.1122942423_4632617350_4340687}+ \ \ \displaystyle {{0.3236128855_0192725686_8232032}\ i}$

(18)

Type: Complex(Float)

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eval(i1,delta=-1)

$\label{eq19}{{\left(- y \right)}^{{1 -{2 \ i}}\over 2}}\over{{\Gamma \left({3 -{4 \ i}}\right)}\ {\cosh \left({\pi}\right)}}$

(19)

Type: Expression(Complex(Integer))

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eval(i1,delta=0)

$\label{eq20}{\sqrt{- y}}\over 2$

(20)

Type: Expression(Complex(Integer))

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eval(i1,delta=1)

$\label{eq21}{{\left(- y \right)}^{{1 +{2 \ i}}\over 2}}\over{{\Gamma \left({3 +{4 \ i}}\right)}\ {\cosh \left({\pi}\right)}}$

(21)

Type: Expression(Complex(Integer))

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integrate(i0,beta=%minusInfinity..%plusInfinity,"noPole")

   >> System error:
   arithmetic error DIVISION-BY-ZERO signalled
Operation was SB-KERNEL::DIVISION, operands (0 0).

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integrate(i1,delta=%minusInfinity..%plusInfinity,"noPole")

   >> System error:
   arithmetic error DIVISION-BY-ZERO signalled
Operation was SB-KERNEL::DIVISION, operands (0 0).

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integrate(x^(t-1)*exp(-x),x=0..%plusInfinity,"noPole")

$\label{eq22}\mbox{\tt "failed"}$

(22)

Type: Union(fail: failed,...)

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integrate(x^((2+%i*2)-1)*exp(-x),x=0..%plusInfinity,"noPole")

$\label{eq23}\mbox{\tt "failed"}$

(23)

Type: Union(fail: failed,...)

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)lib GDRAW

   GnuDraw is now explicitly exposed in frame initial 
   GnuDraw will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/GDRAW.NRLIB/GDRAW
gnuDraw(aa(x,y),x=-30..60,y=-30..30,"SandBoxDoublePowerSeries1.dat",title=="Generating Function")

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Compiling function aa with type (Variable(x),Variable(y)) -> 
      Expression(Integer)

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Compiling function %C with type (DoubleFloat,DoubleFloat) -> 
      DoubleFloat 
   Transmitting data...

Type: Void

[terminal=pslatex,terminaloptions=color,scale=1.3]
set view 60, 30, 0.85, 1.1
set samples 20, 20
set isosamples 21, 21
set contour base
set cntrparam levels auto 20
set title "3D gnuplot demo - contour plot"
set xlabel "X axis"
set ylabel "Y axis"
set zlabel "Z axis"
set zlabel offset character 1, 0, 0 font "" textcolor lt -1 norotate
load "SandBoxDoublePowerSeries1.dat"