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Similar questions have been asked before regarding journals that publish:

However, I did not find any references to journals that publish new mathematical identities. These might include new formulae for $\pi$, $e$, or other known constants that might be useful for researchers in a wide variety of fields.

After briefly looking through papers that contain expositions of new formulae, it would seem that the majority of these papers are given "as-is", i.e., as notes freely available on the webpage of the author. Are there no journals that publish such results?

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    $\begingroup$ In my personal opinion such a journal would be 'neither here nor there', as they say. By this I mean that either the identity should be important or deep enough to find favor with established traditional journals, or you should be bolder and more innovative by designing and creating some kind of 'identity wiki', highly formalized in both its presentation and in the proofs that the wiki demands of its contributors. $\endgroup$ – Peter Heinig Mar 6 '18 at 13:18
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    $\begingroup$ You might be interested to see the H. Wilf and D. Zeilberger algorithm for generating identities... D. Zeilberger has a Wikipedia page, and from there you can find his web-page, which has many documents. $\endgroup$ – paul garrett Mar 6 '18 at 14:00
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As Peter Heinig commented, if the mathematics behind the identity is novel and important enough, then you should select a journal like you would select a journal for any other paper—if it's a combinatorial identity, look for a combinatorics journal; if it's a number-theoretic identity, look for a number theory journal, etc.

For the specific case of constants such as $\pi$ and $e$, most novel identities for them are nowadays discovered with significant computer assistance. The journal Experimental Mathematics is one place where such identities have been published, e.g., I'm fond of Jesús Guillera's paper About a New Type of Ramanujan-Type Series, which contains some amazing identities such as the following one due to Gourevitch (which I believe is still open as of this writing):

$$\sum_{n=0}^\infty \frac{1+14n+76n^2+168n^3}{2^{20n}}\binom{2n}{n}^7 = \frac{32}{\pi^3}.$$

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    $\begingroup$ What do you mean it's open? $\endgroup$ – Monroe Eskew Mar 6 '18 at 15:43
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    $\begingroup$ Open as in it has been confirmed to large precision, but not proven to be true. Gerhard "Some Statements Are Like That" Paseman, 2018.03.06. $\endgroup$ – Gerhard Paseman Mar 6 '18 at 16:07
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    $\begingroup$ Yes Timothy, the formula for 1/pi^3 discovered by Boris Gourevitch using the PSLQ algorithm is still unproved. Also still unproved are the formulas (2-2), (2-3), (2-4) and (2-5) of the paper you cite (I am glad you like it). $\endgroup$ – Jesús Guillera Mar 6 '18 at 23:31
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For new combinatorial identities in the spirit of S. Ramanujan's work, there is the Ramanujan journal.

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The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal (all published by the Mathematical Association of America) might be appropriate.

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    $\begingroup$ I thought the AMM was for expository work, not new original ideas (as stated on their website, Novelty and generality are far less important than clarity of exposition and broad appeal) $\endgroup$ – Klangen Mar 6 '18 at 14:09
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    $\begingroup$ I've read quite a few issues of AMM and while "novelty and generality are far less important," it seems to me that they wouldn't publish anything that is not original. $\endgroup$ – Joel Reyes Noche Mar 6 '18 at 14:14
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    $\begingroup$ @JoelReyesNoche : One has to be careful with the word "original." For example, no journal would knowingly publish plagiarized work. So at least this very low bar of originality must be met. But Monthly articles need not contain theorems or even proofs that are original in the sense that most mathematical researchers use the term "original." There should, however, be at least something original about the way the material is presented. Of course, the Monthly won't reject something for being original, but contrary to popular opinion, it is not primarily a "journal of minor research results" $\endgroup$ – Timothy Chow Mar 6 '18 at 15:04
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    $\begingroup$ @Pickle: The short "Notes" in each issue of AMM frequently include original proofs of mathematical identities. $\endgroup$ – Mark Meckes Mar 6 '18 at 15:09
  • $\begingroup$ @Pickle, there's a nice little counterexample (a new theorem published in the AMM) in the list of papers that originated on math.stackexchange.com $\endgroup$ – Peter Taylor Mar 6 '18 at 17:21

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