The sum of the absolute squares of the spherical harmonics Y_l^m(θ, ϕ) over all values of m is sum_(m = - l)^l ( left bracketing bar Y_l^m(θ, ϕ) right bracketing bar )^2 = (2l + 1)/(4π). The double sum over m and l is given by sum_(l = 0)^∞ sum_(m = - l)^l Y_l^m(θ_1, ϕ_1)Y^__l^m(θ_2, ϕ_2) | = | 1/(sin θ_1) δ(θ_1 - θ_2) δ(ϕ_1 - ϕ_2) | = | δ(cos θ_1 - cos θ_2) δ(ϕ_1 - ϕ_2), where δ(x) is the delta function.
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.
Club Z! has connected me with a tutor through their online platform! This was exactly the one-on-one attention I needed for my math exam. I was very pleased with the sessions and ClubZ’s online tutoring interface.
My son was suffering from low confidence in his educational abilities. I was in need of help and quick. Club Z! assigned Charlotte (our tutor) and we love her! My son’s grades went from D’s to A’s and B’s.
I’ve been using Club Z’s online classrooms to receive some help and tutoring for 2 of my college classes. I must say that I am very impressed by the functionality and ease of use of their online App. Working online with my tutor has been a piece of cake. Thanks Z.
Jonathan is doing really well in all of his classes this semester, 5 A’s & 2 B’s (he has a computer essentials class instead of PLC). In his Algebra class that Nathan is helping him with he has an A+.
Sarah is very positive, enthusiastic and encourages my daughter to do better each time she comes. My daughter’s grade has improved, we are very grateful for Sarah and that she is tutoring our daughter. Way to go ClubZ!
