Return-path: Envelope-to: jbovlaste-admin@lojban.org Delivery-date: Sat, 12 Nov 2022 14:22:07 -0800 Received: from [192.168.123.254] (port=48680 helo=jiten.lojban.org) by d7893716a6e6 with smtp (Exim 4.94.2) (envelope-from ) id 1otyt2-008XSA-R7 for jbovlaste-admin@lojban.org; Sat, 12 Nov 2022 14:22:07 -0800 Received: by jiten.lojban.org (sSMTP sendmail emulation); Sat, 12 Nov 2022 22:22:04 +0000 From: "Apache" To: curtis289@att.net Reply-To: webmaster@lojban.org Subject: [jvsw] Definition Edited At Word gei'au -- By krtisfranks Date: Sat, 12 Nov 2022 22:22:04 +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 "gei'au" in the language "English". Differences: 11,11d10 < Word: hypergeometric function, In Sense: generalized \n12a12,12 \n> Word: hypergeometric function, In Sense: generalized Old Data: Definition: mekso 7-ary operator: for input $(X_1 = z, X_2 = (a_i)_i, X_3 = (b_j)_j, X_4 = p, X_5 = q, X_6 = h_1, X_7 = h_2)$, this word/function outputs/yields $\sum_{n=0}^{\infty} (((\prod_{i = 1}^{p} ($ne'o'o$(a_i,n,1,h_1)))/(\prod_{j = 1}^{q} ($ne'o'o$(b_j,n,1,h_2)))) z^n/(n!))$; by default, $X_6 = 1 = X_7$ unless explicitly specified otherwise. Notes: See "{ne'o'o}" (Pochhammer symbol); however, for the purposes of this definition and regardless of the definition(s) provided at "ne'o'o", here ne'e'o$(Y_1, Y_2, Y_3, Y_4) = \prod_{k = 0}^{Y_2 - 1} (Y_1 + (-1)^{(1 - Y_3)} Y_4 k)$ by local definition; ne'o'o$(Y_1, Y_2, Y_3, Y_4) = 1$ for all $Y_2 < 1$, regardless of the other inputs $Y_m$ (so long as they belong to the domain); by default, $Y_4 = 1$ unless explicitly defined otherwise. For the main definition: $z$ is a complex number, and $(a_i)_i$ and $(b_j)_j$ are (pre)defined sequences (id est: functions with domains being exactly the set of exactly all positive integers) such that, for all positive integer indices $i$ and $j$ respectively, their terms/outputs are complex numbers; both $(a_i)_i$ and $(b_j)_j$ are indexed starting at $1$; also, $p, q, h_1, h_2$ are positive integers; by default, $h_1 = 1 = h_2$ unless explicitly specified otherwise. Jargon: Gloss Keywords: Word: hypergeometric function, In Sense: generalized Word: generalized hypergeometric function, In Sense: Place Keywords: New Data: Definition: mekso 7-ary operator: for input $(X_1 = z, X_2 = (a_i)_i, X_3 = (b_j)_j, X_4 = p, X_5 = q, X_6 = h_1, X_7 = h_2)$, this word/function outputs/yields $\sum_{n=0}^{\infty} (((\prod_{i = 1}^{p} ($ne'o'o$(a_i,n,1,h_1)))/(\prod_{j = 1}^{q} ($ne'o'o$(b_j,n,1,h_2)))) z^n/(n!))$; by default, $X_6 = 1 = X_7$ unless explicitly specified otherwise. Notes: See "{ne'o'o}" (Pochhammer symbol); however, for the purposes of this definition and regardless of the definition(s) provided at "ne'o'o", here ne'e'o$(Y_1, Y_2, Y_3, Y_4) = \prod_{k = 0}^{Y_2 - 1} (Y_1 + (-1)^{(1 - Y_3)} Y_4 k)$ by local definition; ne'o'o$(Y_1, Y_2, Y_3, Y_4) = 1$ for all $Y_2 < 1$, regardless of the other inputs $Y_m$ (so long as they belong to the domain); by default, $Y_4 = 1$ unless explicitly defined otherwise. For the main definition: $z$ is a complex number, and $(a_i)_i$ and $(b_j)_j$ are (pre)defined sequences (id est: functions with domains being exactly the set of exactly all positive integers) such that, for all positive integer indices $i$ and $j$ respectively, their terms/outputs are complex numbers; both $(a_i)_i$ and $(b_j)_j$ are indexed starting at $1$; also, $p, q, h_1, h_2$ are positive integers; by default, $h_1 = 1 = h_2$ unless explicitly specified otherwise. Jargon: Gloss Keywords: Word: generalized hypergeometric function, In Sense: Word: hypergeometric function, In Sense: generalized Place Keywords: You can go to to see it.