## 30 Reputation

9 years, 344 days

## @Kitonum  that,s not the solution. ...

@Kitonum  that,s not the solution. I used the seperators as you can see it again.

> restart;
> m:=2: k:=1.0931: a:=k-m: b:=k+m-1:
> z:=(k*m)/10^(0.1*10):
> simplify(((10^(0.1*yo))^((b-a+2*p-1)/2)*z^((b-a+2*p+1)/2)*GAMMA((1-(b-a+2*p))/2))/(p!*GAMMA(p-a+1)*GAMMA(1+((1-(b-a+2*p))/2))));
> [seq(limit(%,p=kk),kk=0..10)];
1 /
---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) exp(
GAMMA(p + 1.906900000)
p
-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(
\
-1. - 1. p)/
[ / 1 /
[limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
[ \GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 0|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 1|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 2|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 3|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 4|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 5|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 6|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 7|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 8|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 9|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \]
GAMMA(-1. - 1. p)/, p = 10|]
/]

should be something else...

## limits...

why my expression is in terms of limit p approaches to k and not in closed form as yours...?????

## @acer  I am getting my sequence in ...

@acer  I am getting my sequence in terms of limits.... why it is not in closed form....??? am I wrongly putting the limits???/

## @acer  oh.... thanks.... :)...

@acer  oh.... thanks.... :)

## @Markiyan Hirnyk  where am I wrong....

where am I wrong..?? I am getting error for convert command that ) (bracket) is missing.

## @Markiyan Hirnyk  thanks for soluti...

thanks for solution.

I used this for series with unknown parameter and got this

> restart:
> m:=2; k:=1.0931; a:=k-m; b:=k+m-1;
m := 2
k := 1.0931
a := -0.9069
b := 2.0931
> z:=(k*m)/10^(0.1*10);
z := 0.2186200000
> simplify(((10^(0.1*yo))^((b-a+2*p-1)/2)*z^((b-a+2*p+1)/2)*GAMMA((1-(b-a+2*p))/2))/(p!*GAMMA(p-a+1)*GAMMA(1+((1-(b-a+2*p))/2))));
1 /
---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) exp(
GAMMA(p + 1.906900000)
p
-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(
\
-1. - 1. p)/
> [seq(limit(.3183098861*sin(3.141592654*p+3.141592654)*exp(-3.040840432-1.520420216*p+.2302585095*yo)*(exp(.2302585095*yo))^p*GAMMA(-1.-1.*p)/GAMMA(p+1.906900000),p=k),k=0..10)]
Warning, inserted missing semicolon at end of statement, ...=k),k=0..10)];
[ / 1 /
[limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
[ \GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 0|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 1|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 2|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 3|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 4|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 5|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 6|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 7|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 /
GAMMA(-1. - 1. p)/, p = 8|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 9|,
/

/ 1 /
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654)
\GAMMA(p + 1.906900000)

p
exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \]
GAMMA(-1. - 1. p)/, p = 10|]
/]
> convert(%,'+');
Error, `)` unexpected

cant this series be represented as sum of all terms? I need to see the variation with respect to different values of yo.

## @acer  yup i also got such a linear...

@acer  yup i also got such a linear plot...  but its not validating my function. it must become constant at higher values of L. may be some problem in my function. thanks a load for helping.

@acer  would you please upload the plot so that i can interpret my results and validate them.

## @acer  I am using maple 9.5...

@acer  I am using maple 9.5

## another plot...

i have posted another worksheet. see it and help me.

## another plot...

 restart:
 > m:=2; k:=24.503; a:=k-m*L; b:=k+m*L-1;

 > z:=(k*m)/10^(0.1*15);

 > yo:=10^(0.1*10);

 > N1:=sum(((yo^((b-a+2*p-1)/2)*z^((b-a+2*p-1)/2)*GAMMA((1-(b-a+2*p))/2))/(p!*GAMMA(p-a+1)*GAMMA(1+((1-(b-a+2*p))/2)))),p=0..100):
 > N2:=sum(((yo^((b+a+2*p-1)/2)*z^((b+a+2*p-1)/2)*GAMMA((1-(b+a+2*p))/2))/(p!*GAMMA(p+a+1)*GAMMA(1+((1-(b+a+2*p))/2)))),p=0..100):
 > x:=evalf((Pi*csc(a*Pi))/(GAMMA(m*L)*GAMMA(k))):
 > c:=x*(N1-N2):
 > cc:=log[2](1+1/c):
 > me:=MeijerG([[],[1-((b+1)/2)]],[[-(b+1)/2,a/2,-a/2],[]],(z*yo)):
 > m1:=((z*yo)^((b+1)/2))/(GAMMA(m*L)*GAMMA(k)):
 > pp:=m1*me:
 > capacity:=cc*pp:
 > with(plots):

Warning, the name changecoords has been redefined

 > plot(capacity,L=1..4);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Error, empty plot

 >

debug the error in this plot please...

## @Kitonum  that was a silly mistake....

that was a silly mistake. Thanks.

## worksheet attached...

 > restart:
 > m:=2; k:=24.503; a:=k-m*L; b:=k+m*L-1;

 > z:=(k*m)/10^(0.1*15);

 > yo:=10^(0.1*10);

 > N1:=sum(((yo^((b-a+2*p-1)/2)*z^((b-a+2*p-1)/2)*GAMMA((1-(b-a+2*p))/2))/(p!*GAMMA(p-a+1)*GAMMA(1+((1-(b-a+2*p))/2)))),p=0..100):
 > N2:=sum(((yo^((b+a+2*p-1)/2)*z^((b+a+2*p-1)/2)*GAMMA((1-(b+a+2*p))/2))/(p!*GAMMA(p+a+1)*GAMMA(1+((1-(b+a+2*p))/2)))),p=0..100):
 > x:=evalf((Pi*csc(a*Pi))/(GAMMA(m*L)*GAMMA(k))):
 > c:=x*(N1-N2):
 > cc:=log[2](1+1/c):
 > me:=MeijerG([[],[1-((b+1)/2)]],[[-(b+1)/2,a/2,-a/2],[]],(z*yo)):
 > m1:=((z*yo)^((b+1)/2))/(GAMMA(m*L)*GAMMA(k)):
 > pp:=m1*me:
 > capacity:=cc*pp:
 > with(plots):

Warning, the name changecoords has been redefined

 > plot(capacity,L=1..4);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Error, empty plot

 >

any help for plotting this function.