Fourier integrals are generalizations of Fourier series. The series representation f a function is a periodic form obtained by generating the coefficients from the function’s definition on the least period [−L, L]. If a function defined on the set of ...

From The Infinite Looper

The gamma function denoted by Γ(n) is defined by
Γ(n) = ⌠x(n-1) e(-x) dx
Math tutoring on Chegg Tutors
Learn about Math terms like The Gamma Function on Chegg Tutors. Work with live, online Math tutors like Chris W. who can help you at any moment, w...

From The Infinite Looper

The Greek capital letter Σ denotes repeated addition. n general, if f is a function defined on the integers, and if n and k are integers such that n ≥ k, then:
Σf(j)=f(k)+f(k+1)+…+f(n)
Math tutoring on Chegg Tutors
Learn about Math terms like Sigm...

From The Infinite Looper

In this video, we prove a property of the Gamma Function whereby Gamma(x+1) = x*Gamma(x) for x is greater than 0.
Math tutoring on Chegg Tutors
Learn about Math terms like properties of the gamma function on Chegg Tutors. Work with live, online Math tut...

From The Infinite Looper

Suppose there is a largest prime number. Call it p. Let Sp be the set of all primes less than or equal to p, as follows:
Sp = (2,3,5,7,11,13,...,p)
Multiply together all of the elements of Sp, and then add 1. Let the result be called z. Then:
z=(2*3*5*7*1...

From The Infinite Looper

To apply the principle of mathematical induction to a sequence of statements Pn:
1. Write out the statements P1, Pk, and Pk + 1.
2. Show that P1 is true.
3. Assume that Pk is true. From this assumption (it is never necessary to prove Pk explicitly), show ...

From The Infinite Looper

Two column vectors A and B are called orthogonal if A ̅ TB = 0, and A ̅TB is called the scalar product of A and B.
It should be noted also that if A is a unitary matrix then A ̅TA = 1, which means that the scalar product of A with itself is 1 or equiva...

From The Infinite Looper

f(x) = ax + b + R(x)/Q(x) where the degree of R(x) is less than the degree of Q(x). Then x is tending to ∞ or x is tending to -∞, f(x) is tending to ax+b and the line y=ax+b is an oblique asymptote for the graph of function
Math tutoring on Chegg Tut...

From The Infinite Looper

The vector space ν with an inner product is called a (real) inner product space.
Math tutoring on Chegg Tutors
Learn about Math terms like Inner Product Spaces on Chegg Tutors. Work with live, online Math tutors like Chris W. who can help you at any mo...

From The Infinite Looper