ZCubes/E Eulers Number Calculations

E Eulers Number Calculations

Euler’s identity links 5 fundamental mathematical constants, the additive identity 0, the multiplicative identity 1, the number π (π = 3.141...), number e (e = 2.718...), a.k.a. Euler's number, the number i, the imaginary unit of the complex numbers. The video demonstrates the computation of Euler’s number in ZCubes including series involving large numbers.

Video

E Eulers Number Calculations

Code

ef:=(1+1/n)^n;
1...1000000000
1...1000000000@ef

1...10000000000000@ef
1...100000000000000000@ef

units.on;
efunction:=(1d500+1d500/n<>d500)^(n<>d500)
efunction(10000000000000000000000000000000000000000d500)

(1/0!)+(1/1!)+(1/2!)+(1/3!)+(1/4!)+(1/5!)+(1/6!)+(1/7!)+(1/8!)+(1/9!)+(1/10!)+
(1/11!)+(1/12!)+(1/13!)+(1/14!)+(1/15!)+(1/16!)+(1/17!)+(1/18!)+(1/19!)+(1/20!)+
(1/21!)+(1/22!)+(1/23!)+(1/24!)+(1/25!)+(1/26!)+(1/27!)+(1/28!)+(1/29!)+(1/30!)+
(1/31!)+(1/32!)+(1/33!)+(1/34!)+(1/35!)+(1/36!)+(1/37!)+(1/38!)+(1/39!)+(1/40!)+
(1/41!)+(1/42!)+(1/43!)+(1/44!)+(1/45!)+(1/46!)+(1/47!)+(1/48!)+(1/49!)+(1/50!)+
(1/51!)+(1/52!)+(1/53!)+(1/54!)+(1/55!)+(1/56!)+(1/57!)+(1/58!)+(1/59!)+(1/60!)+
(1/61!)+(1/62!)+(1/63!)+(1/64!)+(1/65!)+(1/66!)+(1/67!)+(1/68!)+(1/69!)+(1/70!)+
(1/71!)+(1/72!)+(1/73!)+(1/74!)+(1/75!)+(1/76!)+(1/77!)+(1/78!)+(1/79!)+(1/80!)+
(1/81!)+(1/82!)+(1/83!)+(1/84!)+(1/85!)+(1/86!)+(1/87!)+(1/88!)+(1/89!)+(1/90!)+
(1/91!)+(1/92!)+(1/93!)+(1/94!)+(1/95!)+(1/96!)+(1/97!)+(1/98!)+(1/99!)+(1/100!)

SERIESSTR("1/_x!",1..100)
SERIESSTR("1/_x!",1..100).join("+")

SERIESSTR("(1/_x!)",1..100).join("+")
SERIESSTR("(1/_x!)",0..100).join("+")