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Sep 2, 2021 at 23:54 comment added Somos By the way, $\sum_{j=0}^\infty {2j \choose j} x^j = (1-4x)^{-1/2}$ is well known and your result follows.
Sep 2, 2021 at 4:18 history became hot network question
Sep 1, 2021 at 21:35 comment added Alexandre Eremenko If you really discovered a new identity, just contact the editors of NIST, and ask for inclusion.
Sep 1, 2021 at 21:06 vote accept garserdt216
Sep 1, 2021 at 20:55 answer added Carlo Beenakker timeline score: 11
Sep 1, 2021 at 20:38 comment added garserdt216 @მამუკაჯიბლაძე Thanks! I've removed this part of the question so that more important (soft) question remains.
Sep 1, 2021 at 20:37 history edited garserdt216 CC BY-SA 4.0
proposed unknown result is known and was thus removed. soft question remains relevant.
Sep 1, 2021 at 20:19 comment added მამუკა ჯიბლაძე Sum[Binomial[2j,j](Cos[x]/2)^(2j),{j,0,\[Infinity]}] in Mathematica gives 1/Sqrt[Sin[x]^2]
Sep 1, 2021 at 20:11 history asked garserdt216 CC BY-SA 4.0