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@christianp http://www.m-hikari.com/ams/ams-2012/ams-121-124-2012/elgindiAMS121-124-2012.pdf was one of the papers I had in mind, where for a real \(p\), there is an associated version of \(\sin\), \(\cos\), and \(\pi\). (The usual ones correspond to \(p=2\).)

π. π.@tpfto@mathstodon.xyz@christianp ...and now I just remembered that someone thought to look at a \(q\)-analog of \(\pi\): https://mathworld.wolfram.com/q-Pi.html