Calculate the Product
Calculator for the multiplication with the product symbol Pi, Π. The product is a repeated multiplication with a start value m and an end value n. As running variable, which is increased by 1 in each step, i is used. Only this variable may occur in the product term. The basic arithmetic operations + - * / are allowed, as well as the power function, like pow(2#i) for 2i. Further allowed functions are sin(), cos(), tan(), asin(), acos(), atan(), log() for the natural logarithm and fac() for the factorial. Also, the constants e and pi can be used.
Example: with m=1 and n=10, Π i = 1*2*3*4*5*6*7*8*9*10 = 3628800 = 10! (factorial function)The product symbol Π works in a similar way to the sum symbol Σ, except that no addition, but a multiplication is made. The factorial function is a simple special case of a product with the starting value 1, which is used very frequently in mathematics. Products can of course be very large if the factors are all greater than one. If at least one factor is zero, then the whole product is zero. There are infinite products without an upper limit, which of course only make sense if there are also factors smaller than one and zero cannot occur. An example is the Wallis product discovered in 1655 by the English mathematician John Wallis to determine half the number pi. π/2 = Π (2*i)*(2*i)/((2*i-1)*(2*i+1)) for m=1 and theoretically n=∞. Of course, infinity is not possible with this calculator and you actually need a very high upper limit to get a good approximation for π/2.
Infinite products like the one above that converge to a fixed value converge. An infinite product where all factors are in the interval ]-1;1[ converges to 0. There are also products that jump back and forth between several values, such as pow(-1#i). Such products diverge. Also if the product goes to infinity, it diverges.