See semifactorial in All languages combined, or Wiktionary
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"ref": "1942 February, Giulio Racah, “Theory of Complex Spectra. I”, in Physical Review, volume 61, numbers 3–4, →DOI, page 188:",
"text": "With the symbol n#x21;#x21; we indicate the semifactorial of n, that is the product 1.3.5#x5C;dotsn if n is odd, and the product 2.4.6#x5C;dotsn if n is even.",
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"ref": "1994 January, Alan Edelman, Eric Kostlan, Michael Shub, “How many eigenvalues of a random matrix are real?”, in Journal of the American Mathematical Society, volume 7, number 1, →DOI, pages 250–251:",
"text": "In the formulas above we use the Euler beta function, a Jacobi polynomial evaluated at three, and also the familiar double factorial (also known as the semifactorial) notation defined by n#x21;#x21;#x3D;#x5C;begin#x7B;cases#x7D;#x5C;displaystyle 1#x5C;times 3#x5C;times 5#x5C;times#x5C;dots#x5C;timesn#x26;#x5C;text#x7B;if#x7D;n#x5C;text#x7B;isodd#x7D;,#x5C;#x5C;#x5B;5pt#x5D;#x5C;displaystyle 2#x5C;times 4#x5C;times 6#x5C;times#x5C;dots#x5C;timesn#x26;#x5C;text#x7B;if#x7D;n#x5C;text#x7B;iseven#x7D;.#x5C;end#x7B;cases#x7D;By convention, 0#x21;#x21;#x3D;(-1)#x21;#x21;#x3D;1.",
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"ref": "2009, Keith B. Oldham, Jan C. Myland, Jerome Spanier, An Atlas of Functions, 2nd edition, Springer, →DOI, →ISBN, page 25:",
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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