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Dec 18, 2018 at 20:46 comment added Wolfgang Excellent! So in fact, you use the duplication formula to shift each argument by $\pm\frac12$, and in the process we get even and odd powers of $2$ instead of powers of $7$.
Dec 18, 2018 at 20:30 vote accept Wolfgang
Dec 18, 2018 at 20:13 history answered Noam D. Elkies CC BY-SA 4.0