3daf5f85-42b2-4171-822e-42749feab939 16 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

set 'n' the length of expansion

n 12 :

Optimiz OFF [None]

Thiele continued fraction x g x sin confrac x n convert maple : x 1 x 2^6 x 2^107 / - x 2^68611 / - x 2^21783857 / 1331 x 2^* 607202 / + / + / + / + / + /

Thiele continued fraction x g x cos confrac x n convert maple : 1 x 2^2 - x 2^6 - x 2^103 / x 2^37813 / 177 x 2^* 338 / - / + / + / + / +

Thiele continued fraction x g x tan confrac x n convert maple : x 1 x 2^3 - x 2^5 x 2^7 - x 2^9 x 2^11 / - / + / + / + / + /

Thiele continued fraction x g x exp confrac x n convert maple : 1 x 1 x 2 - x 3 - x 2 x 5 x 2 - x 7 - x 2 x 9 x 2 - x 11 / - / + / + / + / + / + / + / + / + / + / +

x Clear 1

Thiele continued fraction x g x atan confrac x n convert maple : x 1 x 2^3 x 2^54 / x 2^289 / x 2^8164 / 225 x 2^* 704 / + / + / + / + / + /

Thiele continued fraction x g x asin confrac x n convert maple : x 1 x 2^6 - x 2^1017 / x 2^4046549 / - x 2^6028021173833 / 12889271025 x 2^* 104890816822 / - / + / + / + / + /

Thiele continued fraction x g x acos confrac x n convert maple : π 2 / x 1 - x 2^6 x 2^1017 / - x 2^4046549 / x 2^6028021173833 / - 12889271025 x 2^* 104890816822 / + / + / + / + / + / +

Thiele continued fraction x Ln 1 x + ln confrac x n convert maple : x 1 x 2 x 3 x 1 x 5 x 23 / x 7 x 12 / x 9 x 25 / x 11 / + / + / + / + / + / + / + / + / + / + /

x f x sqrt :

Thiele continued fraction x SQRT 1 x + f confrac x n convert maple : 1 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 / + / + / + / + / + / + / + / + / + / + / + / + / +

x λ 10 x ≤ (x 4 ≤ (& cases :

x 1 - Ln x λ * x ln 2 1 sys x 1 - SQRT x λ * x sqrt 2 1 sys

set 'n' the length of expansion

n 10 :

Optimiz OFF [None]

Thiele continued fraction x g x exp confrac x n convert maple : 1 x 1 x 2 - x 3 - x 2 x 5 x 2 - x 7 - x 2 x 9 / + / + / + / + / + / + / + / + / +

Optimiz NONE

Padé rational fraction x g confrac x convert maple x 5 / 495 / + 12245 x 85351 / - 1876212601 x 711455195279 / - 41417793614661241 x 37686194931943489359 / - 3461343788889257628320041 x 858879507571 / - (* / + (* / + (* / + (* / +

Maple does not expand in continued fraction "ladder style" Expansion of p(x) is in advanced numerical maths J_Fraction

x p 3 x 3^* 10 x 2^* + 12 + 3 x 2^* 2 x 2^* - 12 - / :

x p confrac x convert maple 3 x * 10 + 36 x 113 / - 139 x 113 / + (* / + / +

x S 3 x 3^* 10 x 2^* + 12 + 3 x 2^* 2 x 2^* - 12 - / parfrac x convert maple : 3 x * 10 + 13236 x * + x 2^12 - / +

x S x 3^x + x 2^3 x * - 2 + / parfrac x convert maple : x 3 + 2 x 1 - / - 10 x 2 - / +

t f t a i b * + (* exp :

t f trig convert maple t a * cosh t a * sinh + (i t b * sin * t b * cos + (*

x sin x cos * exp convert maple i 1 - i x * exp 2^+ (* 1 i x * exp 2^+ (* 4 i x * exp 2^* / -

x 1 + (x 2 + (* expand maple 2 x 3 x + (* +

x 1 + (x 2 + (* expand maple x 2^3 x * + 2 +

x 1 + x 2 + / expand maple 2 x + x 2 x + (* + 2 x + (2^/

x 1 + x 2 + / expand maple 1 x * x 2 + / 1 x 2 + / +

β 3 el x 2^(* β 2 el x * + β 1 el + β 6 el x 2^(* β 4 el x * + 1 + / expand maple 1 β 3 el * x 2^* β 6 el x 2^* β 4 el x * + 1 + / 1 β 2 el * x * β 6 el x 2^* β 4 el x * + 1 + / + 1 β 1 el * β 6 el x 2^* β 4 el x * + 1 + / +

x sin (2^exp convert maple 1 - i x * exp 2^+ (2^4 i x * exp 2^* / -

x asin ln convert maple i 1 x 2^- sqrt i x * + ln * -

z H z i ρ * - (z i ρ * + (* z ρ + (* z 3^/ :

z H parfrac z convert maple 1 ρ 3^z 3^/ + ρ 2^z 2^/ + ρ z / +

x f x 1 x 2^+ (* 1 - x + (2 - x + (* / :

Explode for exploring the term by term composition.

x expr x f op maple :

x collect x expr 1 el x expr 2 el x expr 3 el x expr 4 el x f 51 sys :

x collect

x expr x 1 x 2^+ 11 - x + / 12 - x + / 41 mat

If you have a true partial fraction from source it's wise to simplify first to reduce the otherwise long expansion. For this univariate 'x' example: maple(,) simplify = factor. As a rule,, start assume (x>0) in Lapalce .

x 3 + 2 x 1 - / - 10 x 2 - / + simplify maple x 1 x 2^+ (* 1 - x + (2 - x + (* /

x x 2^1 + x 1 - (x 2 - (* / * x 0 > assume x s laplace maple x 1 x 2^+ (* 1 - x + (2 - x + (* s * /

x 3 + 2 x 1 - / - 10 x 2 - / + (x 0 > assume x s laplace factor maple x 1 x 2^+ (* 1 - x + (2 - x + (* s * /

x 3 + 2 x 1 - / - 10 x 2 - / + (x 0 > assume x s laplace simplify maple x 1 x 2^+ (* 1 - x + (2 - x + (* s * /

0 x < x 3 + 2 x 1 - / - 10 x 2 - / + Unwanted if 0 x < x x 2 ^ 1 + x 1 - ( x 2 - ( * / * Unwanted if

Sanity check

x acos x sin * exp convert maple i x acos * i x * exp 1 i x * exp / - (* 2 / -

x sin x acos * exp convert maple i i x * exp 1 i x * exp / - (* x acos * 2 / -

x sin x atan * exp convert maple i i x * exp 1 i x * exp / - (* x atan * 2 / -

x sin exp convert maple i i x * exp 1 i x * exp / - (* 2 / -

x cos exp convert maple i x * exp 2 / 12 i x * exp * / +

n 12 :

Thiele continued fraction x g x exp confrac x n convert maple :

Optimiz NONE

J_Frac piecewise x collect x g confrac x convert maple :

Optimiz NONE

J_Frac expanded x J_Frac x collect expand maple :

x g 1 x 1 x 2 - x 3 - x 2 x 5 x 2 - x 7 - x 2 x 9 x 2 - x 11 / - / + / + / + / + / + / + / + / + / + / +

x collect x 6 / - 716 / - 25556 x 175573 / - 7918405329 x 91506291806385 / - 35540459019612315025 x 12083495748749577127145 / - 1276917665261004014096397441 x 643629406036131369242178451835 / - 57162792361422133133965249672323225 x 315657529184296635 / - (* / + (* / + (* / + (* / + (* / -

x J_Frac x 6 / - 716 / - 25556 x * 1053073 / - 47510405329 x * 66799591724745 / - 189395106112251612315025 x * 29900610230158152003521 / - 781875872127230846525004014096397441 x * 1289525031210915217251184296635 / - 229456958885652497704151601397133965249672323225 x * 58174620407114915 - / + / + / + / + / -

x parfrac x g parfrac x convert maple :

x parfrac 716 / - x 6 / - 1552320 x * 378000 x 2^* - 28000 x 3^* + 2555 x 4^* - 4268880 - 332640 - 151200 x * + 30240 x 2^* - 3360 x 3^* + 210 x 4^* - 6 x 5^* + / +

n 11 :

optimiz NONE x Taylor x cos x n series maple : 1 x 2^2 / - x 4^24 / + x 6^720 / - x 8^40320 / + x 10^3628800 / -

u 0.25 :

u cos u Taylor 21 mat 0.968912421710645 0.968912421710645 21 mat

x cos x 13 taylor polynom convert maple 1 x 2^2 / - x 4^24 / + x 6^720 / - x 8^40320 / + x 10^3628800 / - x 12^479001600 / +

code reported
from Alvaro. e x^x 7 taylor polynom convert maple 1 x + x 2^2 / + x 3^6 / + x 4^24 / + x 5^120 / + x 6^720 / +

x sqrt x 3 taylor polynom convert maple Error, does not have a taylor expansion, try series() ans

x f x 0.25^x n series polynom maple : x 0.25^x 11 series polynom maple

traditional code e x^x 7 taylor confrac convert maple 1 x 1 x 2 - x 3 - x 2 x 5 x 2 / - / + / + / + / + / +

x f x sqrt :

traditional code x f confrac x 7 convert maple Error, (in convert/confrac) wrong number (or type) of parameters in function ser

x f x sqrt :

Thiele continued fraction x SQRT 1 x + f confrac x n convert maple : 1 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 / + / + / + / + / + / + / + / + / + / + / + / +

Thiele continued fraction x Ln 1 x + ln confrac x 15 convert maple : x 1 x 2 x 3 x 1 x 5 x 23 / x 7 x 12 / x 9 x 25 / x 11 x 13 / x 137 x * 2 / + / + / + / + / + / + / + / + / + / + / + / + / + /