(Veronica) Change the computation with Sauzin to be in line with convention- (Aaron) Finish switching the Airy and Airy-Lucas sections to the literature sign convention
- (Aaron) Look over "Why does Borel summation work for solutions of certain level-1 ODEs?"
- (Aaron) Understand new material in "A new perspective: Borel regularity"
- (Aaron) Proofread copied-in sections about Laplace transform
- (Aaron) Check the Bessel equation in the spatial domain that corresponds to the Airy-Lucas equation in the frequency domain
- (Aaron) Look over general modified Bessel example
- (Aaron) Draw position domain picture for Watson-Nevanlinna-Sokal theorem.
(Veronica) Turn Nevanlinna-Watson bullet points into prose
- Prove Theorem 2 (from outline)
- Ask Fredrick whether existence and uniqueness appendix might be publishable on its own
(Veronica) Get in touch- (Aaron) Send summary of existence and uniqueness results
- Airy-Lucas
- (Aaron) Plot Λ(k) contours
- (Aaron) Copy the hypergeomtric function identity used in the contour argument into an appendix
(Veronica) Copy in asymptotic analysis- Show how the proof of Theorem 2 works by going through it in this special case
(Veronica) Construct W̃1 and W̃−1 in the "Asymptotic analysis" section- (Aaron) Revise the "Borel regularity" section to mirror the proof of Theorem 2
- (Aaron) Confirm the uniqueness argument by showing explicitly that ṽ1 sums to a multiple of v1
- General modified Bessel
- (Aaron) Plot contours
- (unassigned) Generalize the differential equation argument used for Airy-Lucas
- (Aaron) Add vibrating beam example
- Fix mistaken coefficients in hyper-Airy 5 example
- (Aaron) Check over the Sage notebook that gave the coefficients in the current draft
- (both) Compare with the Mathematica notebook that gives different coefficients
- Generalized Airy
- (Veronica) Try to do contour argument
- Hyper-Airy
- Try to do contour argument (stuck right now)
- Try plugging ζ = 27u4 − 4u into a generic hypergeometric series in ζ and comparing with the power series of 1 / 4(27u3 − 1)
(Veronica) Write out the comparison with Mariño in the desired way
- The sentence that starts "The Borel transform maps..."
- Thimble integral proof