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gh-39732: Update docstring on E2 <!-- ^ Please provide a concise and informative title. --> <!-- ^ Don't put issue numbers in the title, do this in the PR description below. --> <!-- ^ For example, instead of "Fixes #12345" use "Introduce new method to calculate 1 + 2". --> <!-- v Describe your changes below in detail. --> <!-- v Why is this change required? What problem does it solve? --> <!-- v If this PR resolves an open issue, please link to it here. For example, "Fixes #12345". --> Update docstring on the weight 2 Eisenstein series - replace with specific numbers for $k = 2$. ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [x] The description explains in detail what this PR is about. - [ ] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [x] I have updated the documentation and checked the documentation preview. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - #12345: short description why this is a dependency --> <!-- - #34567: ... --> None URL: #39732 Reported by: Seewoo Lee Reviewer(s): Frédéric Chapoton
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src/sage/modular/quasimodform/ring.py

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.. MATH::
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E_2(z) = 1 - \frac{2k}{B_k} \sum_{n=1}^{\infty} \sigma(n) q^n
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E_2(z) = 1 - 24 \sum_{n=1}^{\infty} \sigma(n) q^n
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where `\sigma` is the sum of divisors function and `q = \mathrm{exp}(2\pi i z)`
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is the classical parameter at infinity, with `\mathrm{im}(z)>0`. This weight 2
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.. MATH::
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z^2 E_2(-1/z) = E_2(z) + \frac{2k}{4\pi i B_k z}.
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z^2 E_2(-1/z) = E_2(z) + \frac{6}{\pi i z}.
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`E_2` is a quasimodular form of weight 2. General quasimodular forms of given
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weight can also be defined. We denote by `QM` the graded ring of quasimodular

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