Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Tue, 13 Dec 2022 14:02:10 -0800 Received: from [192.168.123.254] (port=49478 helo=web.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1p5DLk-009frz-5A for jbovlaste-admin@lojban.org; Tue, 13 Dec 2022 14:02:10 -0800 Received: by web.lojban.org (sSMTP sendmail emulation); Tue, 13 Dec 2022 22:02:08 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word ne'o'au -- By krtisfranks Date: Tue, 13 Dec 2022 22:02:07 +0000 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Message-Id: X-Spam-Score: -2.9 (--) X-Spam_score: -2.9 X-Spam_score_int: -28 X-Spam_bar: -- In jbovlaste, the user krtisfranks has edited a definition of "ne'o'au" in the language "English". Differences: 5,5c5,5 < By default, $X_2 = -1$ (notice the double-negative). Inherits the defaults for/of "{ne'o'a}" (for: $X_3 =$ ne'o'a$_2$, and $X_4 =$ ne'o'a$_3$). The 0th derivative is the identity operator; negative-integer-order derivatives (meaning: integer-valued $X_2$ such that $0 < X_2$) are antiderivatives. $X_2$ being other than a non-positive integer, or $X_1$ being non-real, should require mention or assumption of the cultural default interpretation of the definition of the differintegral operator. "Log" here denotes the primary branch of the natural (base-$e$) logarithm. This is a shift of the polygamma function by 1, so as to be consistent with "{ne'o}". --- > By default, $X_2 = -1$ (notice the double-negative). Inherits the defaults for/of "{ne'o'a}" (for: $X_3 =$ ne'o'a$_2$, and $X_4 =$ ne'o'a$_3$). The 0th derivative is the identity operator; in order to be consistent with "{salri}", negative-integer-order derivatives (meaning: positive $X_2$) are antiderivatives. $X_2$ being other than a non-positive integer, or $X_1$ being non-real, should require mention or assumption of the cultural default interpretation of the definition of the differintegral operator. "Log" here denotes the primary branch of the natural (base-$e$) logarithm. This is a shift of the polygamma function by 1, so as to be consistent with "{ne'o}". Therefore, the basic digamma function, often denoted "$\psi_0 (z)$,is equal to this word's output for $X_1 = z - 1, X_2 = -1, X_3 = 0, X_4 =$ +infty (notice the prevalence of the default parameter values). 12,12d11 < Word: polygamma function, In Sense: \n13a13,13 \n> Word: polygamma function, In Sense: Old Data: Definition: mekso quaternary operator: polygamma function; for input $X_1, X_2, X_3, X_4$, outputs the $(-X_2)$th derivative of Log(ne'o'a($X_1, X_3, X_4$)) with respect to $X_1$. Notes: By default, $X_2 = -1$ (notice the double-negative). Inherits the defaults for/of "{ne'o'a}" (for: $X_3 =$ ne'o'a$_2$, and $X_4 =$ ne'o'a$_3$). The 0th derivative is the identity operator; negative-integer-order derivatives (meaning: integer-valued $X_2$ such that $0 < X_2$) are antiderivatives. $X_2$ being other than a non-positive integer, or $X_1$ being non-real, should require mention or assumption of the cultural default interpretation of the definition of the differintegral operator. "Log" here denotes the primary branch of the natural (base-$e$) logarithm. This is a shift of the polygamma function by 1, so as to be consistent with "{ne'o}". Jargon: Gloss Keywords: Word: digamma function, In Sense: Word: polygamma function, In Sense: Word: polyfactorial, In Sense: Word: poly-pi function, In Sense: related to the factorial Place Keywords: New Data: Definition: mekso quaternary operator: polygamma function; for input $X_1, X_2, X_3, X_4$, outputs the $(-X_2)$th derivative of Log(ne'o'a($X_1, X_3, X_4$)) with respect to $X_1$. Notes: By default, $X_2 = -1$ (notice the double-negative). Inherits the defaults for/of "{ne'o'a}" (for: $X_3 =$ ne'o'a$_2$, and $X_4 =$ ne'o'a$_3$). The 0th derivative is the identity operator; in order to be consistent with "{salri}", negative-integer-order derivatives (meaning: positive $X_2$) are antiderivatives. $X_2$ being other than a non-positive integer, or $X_1$ being non-real, should require mention or assumption of the cultural default interpretation of the definition of the differintegral operator. "Log" here denotes the primary branch of the natural (base-$e$) logarithm. This is a shift of the polygamma function by 1, so as to be consistent with "{ne'o}". Therefore, the basic digamma function, often denoted "$\psi_0 (z)$,is equal to this word's output for $X_1 = z - 1, X_2 = -1, X_3 = 0, X_4 =$ +infty (notice the prevalence of the default parameter values). Jargon: Gloss Keywords: Word: digamma function, In Sense: Word: polyfactorial, In Sense: Word: polygamma function, In Sense: Word: poly-pi function, In Sense: related to the factorial Place Keywords: You can go to to see it.