gei'au

valsi

gei'au

type

experimental cmavo

creator

krtisfranks

time entered

Sat Nov 12 21:28:56 2022  

English

Definition #73028 - Preferred

 

selma'o

VUhU3

definition

mekso 7-ary operator: for input MATH

$(X_1 = z, X_2 = (a_i)_i, X_3 = (b_j)_j, X_4 = p, X_5 = q, X_6 = h_1, X_7 = h_2)$

(X₁ = z, X₂ = (a_i)_i, X₃ = (b_j)_j, X₄ = p, X₅ = q, X₆ = h₁, X₇ = h₂), this word/function outputs/yields MATH

$\sum_{n=0}^{\infty} (((\prod_{i = 1}^{p} ($

<img alt="$\sum_Template:n=0^Template:\infty$" src="/jbovlaste_export/oOYGQcM56a/img1.png" style="height: 2.66ex; vertical-align: -0.81ex; "/>(((<img alt="$\prod_Template:i = 1^Template:p$" src="/jbovlaste_export/oOYGQcM56a/img2.png" style="height: 2.66ex; vertical-align: -0.81ex; "/>(ne'o'o MATH

$(a_i,n,1,h_1)))/(\prod_{j = 1}^{q} ($

(a_i, n, 1, h₁)))/(<img alt="$\prod_Template:j = 1^Template:q$" src="/jbovlaste_export/oOYGQcM56a/img3.png" style="height: 3.01ex; vertical-align: -1.13ex; "/>(ne'o'o MATH

$(b_j,n,1,h_2)))) z^n/(n!))$

(b_j, n, 1, h₂))))zⁿ/(n!)); by default, MATH

$X_6 = 1 = X_7$

X₆ = 1 = X₇ 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 MATH

$(Y_1, Y_2, Y_3, Y_4) = \prod_<a class="undefined" href="../dict/k%20%3d%200?bg=1;langidarg=2">k = 0</a>^<a class="undefined" href="../dict/Y_2%20-%201?bg=1;langidarg=2">Y_2 - 1</a> (Y_1 + (-1)^<a class="undefined" href="../dict/(1%20-%20Y_3)?bg=1;langidarg=2">(1 - Y_3)</a> Y_4 k)$

(Y₁, Y₂, Y₃, Y₄) = <img alt="$\prod_Template:k = 0^Template:Y 2 - 1$" src="/jbovlaste_export/blRiJYDuqd/img1.png" style="height: 3.01ex; vertical-align: -0.81ex; "/>(Y₁ + (- 1)^(1-Y₃)Y₄k) by local definition; ne'o'o MATH

$(Y_1, Y_2, Y_3, Y_4) = 1$

(Y₁, Y₂, Y₃, Y₄) = 1 for all Y₂ < 1, regardless of the other inputs Y_m (so long as they belong to the domain); by default, Y₄ = 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, MATH

$p, q, h_1, h_2$

p, q, h₁, h₂ are positive integers; by default, MATH

$h_1 = 1 = h_2$

h₁ = 1 = h₂ unless explicitly specified otherwise. X₂ and X₃ may require usage of "mau'au" and "zai'ai".

gloss words

• generalized hypergeometric function
• hypergeometric function ; generalized

created by

krtisfranks

vote information

1

time

Sat Nov 12 22:55:55 2022

Examples

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