## is it possible to evaluate or how to evaluate this...

updated

after refer from

https://en.wikipedia.org/wiki/List_of_representations_of_e

exponential1 := sum((1/n!), n=0..infinity);
exponential1 is not a decimal number, it is exp(1)

hoyeung1:= sum((Int(exp(LambertW(1/(-1+x))*(-1+x)), x)), x=0..infinity);

hoyeung2:= sum((Int(exp(LambertW(1/(-1+x!))*(-1+x!)), x)), x=0..infinity);

how to evalute hoyeung1 or hoyeung2 as a decimal number?

how to evalute hoyeung^x as a decimal number function is func1 := proc(x) return hoyeung^x end proc:

but i do not know whether sum((Int(exp(LambertW(1/(-1+x))*(-1+x)), x))*m^x, x=0..infinity) = hoyeung^x

can limit(1+(Int(exp(LambertW(1/(-1+x))*(-1+x)), x)))^x, x=infinity) = hoyeung^1 ?

## Summation giving unexpected result...

I am trying to evaluate the following summation which gives the result 0. But I think answer is not correct.

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## Partial derivative of multivariable function using...

Problem.mw

Hi,

I want to know the partial derivative of

where

in order to

ρ

If I write

I obtain this

which is incorrect  since I did not have any indexes in sigma. However if I do this next command the result seems correct although no substituion of rhocrf

What I would like to obtain was the solution in order to rho and not to rhocrf and additionally having the result as a summation over p and q and not the extended result. How should I write it in Maple then?

Thank you very much!

## Convert series to function...

Good day everyone,

I'm trying to convert a series solution back to its original function but its given me "Error, (in rsolve/linindex) invalid subscript selector".

Anyone with useful informations please.

Attached is the series below

theta := convert(a-(1/2)*beta*a^2*y^2+(1/12)*beta^2*a^3*y^4-(1/72)*beta^3*a^4*y^6+(1/504)*beta^4*a^5*y^8-(5/18144)*beta^5*a^6*y^10+(1/27216)*beta^6*a^7*y^12-(95/19813248)*beta^7*a^8*y^14+O(y^16), polynom);
1       2  2   1      2  3  4   1      3  4  6
a - - beta a  y  + -- beta  a  y  - -- beta  a  y
2              12               72

1      4  5  8     5       5  6  10     1       6  7  12
+ --- beta  a  y  - ----- beta  a  y   + ----- beta  a  y
504               18144                27216

95        7  8  14
- -------- beta  a  y
19813248
L := [seq(coeff(theta, y, n), n = 0 .. 14)];
[        1       2     1      2  3       1      3  4
[a, 0, - - beta a , 0, -- beta  a , 0, - -- beta  a , 0,
[        2             12                72

1      4  5         5       5  6       1       6  7
--- beta  a , 0, - ----- beta  a , 0, ----- beta  a , 0,
504                18144              27216

95        7  8]
- -------- beta  a ]
19813248         ]
with(gfun);
rec := listtorec(L, u(n));
[ //      2     2  3         2     2  2          2     2  \
[{ \2151 a  beta  n  - 1434 a  beta  n  - 30592 a  beta  n/ u(n) +
[ \

/             3                  2
\2476 a beta n  - 137904 a beta n  + 207248 a beta n

\
+ 424320 a beta/ u(n + 2)

/         3           2                      \
+ \-153660 n  - 322920 n  + 1803360 n + 2545920/ u(n + 4),

1       2          \      ]
u(0) = a, u(1) = 0, u(2) = - - beta a , u(3) = 0 }, ogf]
2                  /      ]

rsolve(rec[1], u);
/ //      2     2  3         2     2  2          2     2  \
rsolve|{ \2151 a  beta  n  - 1434 a  beta  n  - 30592 a  beta  n/
\ \

/             3                  2
u(n) + \2476 a beta n  - 137904 a beta n  + 207248 a beta n

\
+ 424320 a beta/ u(n + 2)

/         3           2                      \
+ \-153660 n  - 322920 n  + 1803360 n + 2545920/ u(n + 4),

1       2          \    \
u(0) = a, u(1) = 0, u(2) = - - beta a , u(3) = 0 }, u|
2                  /    /
sum(%*y^n, n = 0 .. infinity);
Error, (in rsolve/linindex) invalid subscript selector

thanx

## Maple too slow for the calculation of product of s...

I am trying to evaluate the following function J(n,phi) which can be used to find out a*b(-A*J(3,Pi/6)+B*J(6,Pi/6)) but it takes too much of time whereas mathematica takes much less time for the same. The maple file is attached. Hope my problem get solve. Thank you

restart;

r := 2.8749; a := 0.7747; b := 0.3812; A := 17.4; B := 29000; R := 5.4813; Z := 2;

J := proc (n, phi) options operator, arrow; 8*Pi^(3/2)*r*R*(sum((2*r*R)^(2*i)*pochhammer((1/2)*n, i)*pochhammer((1/2)*n+1/2, i)*(sum((-1)^j*cos(phi)^(2*j)*(sum((2*r*cos(phi))^(2.*l)*pochhammer(n+2*i, 2*l)*hypergeom([2*j+2*l+1, .5], [2*j+2*l+1.5], -1)*(.5*Beta(l+.5, n+2*i+l-.5)-sin(arctan(-Z/sqrt(R^2+r^2)))^(2*l+1)*hypergeom([-n-2*i-l+1.5, l+.5], [l+1.5], sin(arctan(-Z/sqrt(R^2+r^2)))^2)/(2*l+1))/(factorial(2*l)*pochhammer(2*j+2*l+1, .5)*(R^2+r^2)^(n+2*i+l-.5)), l = 0 .. 100))/(factorial(i-j)*factorial(j)), j = 0 .. i))/factorial(i), i = 0 .. 100)) end proc;

evalf(a*b*(-A*J(3, (1/6)*Pi)+B*J(6, (1/6)*Pi)));
JJ.mw

## if condition inside eval and sum...

I really want to use if condition inside of eval and sum, example as below:

sum(eval(y=x^(j),(if j=1 then x=2 else x=3 fi)),j=1..2)

The reason is: the value of x to be evaluated depends on the value of j which differs inside of the sum (in the context of B-spline functions).

Any lights? Thanks,

## how must i write this formula?...

any idea for my problem?

> k1 := sum(X[h, t], t = 1 .. 23) >= 9;
9 <= X[h, 1] + X[h, 2] + X[h, 3] + X[h, 4] + X[h, 5] + X[h, 6]

+ X[h, 7] + X[h, 8] + X[h, 9] + X[h, 10] + X[h, 11] + X[h, 12]

+ X[h, 13] + X[h, 14] + X[h, 15] + X[h, 16] + X[h, 17]

+ X[h, 18] + X[h, 19] + X[h, 20] + X[h, 21] + X[h, 22]

+ X[h, 23], h = 1 .. 6

why 'h' still 'h'. from my textbooks the formula must be like this :

## solve a system of equation numericlly ...

i want to solve the system of equation ( 1 )  , (2)  ,  (3)   under the assumation that x , y have the CDF in (4)  ,  (5)

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## SEEMOUS 2017

by: Maple

Here is a problem from SEEMOUS 2017 (South Eastern European Mathematical Olympiad for University Students)
which Maple can solve (with a little help).

For k a fixed nonnegative integer, compute:

Sum( binomial(i,k) * ( exp(1) - Sum(1/j!, j=0..i) ), i=k..infinity );

(It is the last one, theoretically the most difficult.)

## Code works fine in Maple 18 and Maple 2015 but not...

I have the following function which came from a collaborator of a collaborator. It computes a generating function for a family of function's we're using.

```GF_Generate := proc (n)
local summand, i, j;
summand := U[0]^x[0]*mul(U[i]^y[i], i = 1 .. n)*mul(binomial(x[0]+add(w[j], j = 1 .. i), y[i])*p^y[i]*(1-p)^(x[0]+add(w[j], j = 1 .. i)-y[i])*binomial(x[0]-1+add(w[j], j = 1 .. i), x[0]-1+add(w[j], j = 1 .. i-1))*v[i]^(x[0]+add(w[j], j = 1 .. i-1))*(1-v[i])^w[i], i = 1 .. n);

for j from n by -1 to 1 do summand := normal(sum(summand, y[j] = 0 .. infinity)) end do;
for j from n by -1 to 1 do summand := normal(sum(summand, w[j] = 0 .. infinity)) end do;

sum(summand, x[0] = 0 .. infinity)
end proc;```

For arguments of 2 and 3 it's quick and works fine on Maple18 (tested both GUI and terminal client on OS X), Maple2015 (tested terminal client only on RHEL linux), but generates a "too many levlels of recursion" error in Maple2016 (tested terminal client only on RHEL linux; same server as Maple2015 was tested). It's slow for arguments of 4 and above (45 minutes for n=4 on my mac laptop), so I haven't tested it thoroughly with larger arguments.

Any idea why this code fails in Maple 2016?

## Problem with finite sum. Negative upper limit...

Hi Dears,

I'm have a code like this:

sum(-GAMMA(k+1, x), k = 0 .. -2) and Maple give me : Ei(1, x).

How to check that answer is correct?

Thank you in advance.

I am looking forward to hearing from you.

## How to expand a double sum for a list of sequences...

Can somebody please expand the following double sum to produce a list of sequences?

(Sum(f[i], i = 0 .. 1))*(Sum(g[i, j, k], j = 0 .. 1)) for k = {1,2}

I need to make sure the operation order is correct, so I would like to verify my workings.

Thanks!

## How to change summation index of Sum from PDE sol...

Hello.

I have a Pde solution in from of the sum.

pde := diff(u(x, t), t) = diff(u(x, t), x\$2)

symbolic := pdsolve([pde, u(x, 0) = 1, u(0, t) = 0, u(1, t) = 0])

symbolic := u(x, t) = Sum(-(2*((-1)^_Z9-1))*sin(_Z9*Pi*x)*exp(-Pi^2*_Z9^2*t)/(Pi*_Z9), _Z9 = 1 .. infinity)

I tried a subs or eval command dosen't work.

Thanks.

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## closed form solution...

I am having issues with Maple 2016 computing closed form solutions using the sum command. For example, sum((-1)^n, n = 1 .. infinity) evaluates to -1/2 in the help topic, however, when I run the command in a maple document, this result is not obtained. It instead returns sum((-1)^n, n = 1 .. infinity). Likewise, sum( a*r^k, k = 0..infinity) doesn't evaluate to -a/(r-1). How can I get Maple to determine closed form solutions for power series?

## double summation problem ...

i wrote this problem to solve

Delta= Sum(j=1 to n)SUM(i=j to n)(pi*hj/Ad(t,ij)*Et,ij))

Where n=70,  G= ftj (t)/(4+0.85*t) , where (t =8, 16, 24,…….up to 8*n), hj= 13 for all j except j1 =18

Ad= (Aj+s(mij-1)), where Aj varies

Mij=ES/E(G),          where E(G)= 57sqrt(1000*G)

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