## 400 Reputation

16 years, 71 days

## approximation with maple...

Maple

i have

p(n):= (2310*n^5+5775*n^4+5019*n^3+(3507/2)*n^2+(409/2)*n+5/2)/(27720*n^7+97020*n^6+132300*n^5+88200*n^4+29400*n^3+4410*n^2+210*n)

how can apprximate p(n) with another polynomial (say: a second degree polynomial in n) or a rational function (ration of two second order polynomials) of less degree of n? and how good is that approximation

## how to manupulate algebraic expression...

Maple

I have:

a(n):=(27720*n^(6)+83160*n^(5)+93030*n^(4)+47460*n^(3)+10689*n^(2)+819*n+5)/(27720*n^(7)+97020*n^(6)+132300*n^(5)+88200*n^(4)+29400*n^(3)+4410*n^(2)+210*n):

now i want to multiply by (n+1/2) that is

a(n)*(n+1/2)

now i want to express it in a simples form. may be like this:

c(n) + d(n)/p(n)

## how to find with maple...

Maple

How can i find:

int(x*sinh(x)/sqrt(1-sinh(x)*sinh(x)), x = 0 .. log(sqrt(2)+1))

int(x*sinh(x)/sqrt(1-sinh(x)^2), x = 0 .. ln(sqrt(2)+1))

with maple

## nth derivative of 1/sqrt(1-x^2) and 1/sq...

1/sqrt(1-x^2) and 1/sqrt(1+x^2)

## how to find nth derivative...

Maple

1/(1+x^2)

when i do

diff(1/(1+x*x), `\$`(x, n))

maple gives

diff(1/(1+x^2), `\$`(x, n))

even if i do

value(%)

maple still gives the same answer.

thanks

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