Introduction to product sum identities -- Number Theory 31

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[krisbrandenberger]

Hey, Michael! @ 15:40 I am having trouble understanding how the constant term A_0 can be equal to 1 after expanding everything out. Would you please explain that in full detail for me? Thank you. 😊

[ahoj]

Still following Euler's steps, on the very arduous path to Ramanujan's identities on modular forms! Those are the first q-hypergeometric identities. The A(z) are sometimes referred to as q-exponentials. Now you should also present bijective proofs of all these identities

[aleksandervadla]

Could u do more complex or harmonic analysis?

[krisbrandenberger]

Actually, @ 15:40 I have figured it out. If you take the equation
A(z)=(az)_inf/(z)_inf, multiply it by (z)_inf, and then expand both sides and compare coefficients, we will see that the constant term A_0=1.

[krisbrandenberger]

Hey, Michael! @ 25:19 You could have just rewritten -(-1)^(n-1) as (-1)^n and canceled all of the (-1)^n terms from both sides of the equation.