Alpha Spreadsheet q4.0
- 1 Alpha function code (Spreadsheet) version 4.0
- 2 Javascript code in Google Sheets
- 3 DRAFT Version 4.0 Examples
- 4 Code changes (in this version)
- 5 Notation and Recursion & Summation Functions
- 6 Further References
Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.
You are free to use and copy the code as you like. Version 4.0 of the Javascript code in Google Sheets is available here:
Alpha Function Spreadsheet
Version 4.0 is a complete rewrite of the code to better support the full notation of the Quantum Function. It replaces the Version 3.0 spreadsheet.
Some examples taken from the spreadsheet.
\(\alpha(0) = 0\)
\(\alpha(1) = 1\)
\(\alpha(1.5) = 4\)
\(\alpha(1.6) = 5\)
\(\alpha(1.7) = 6\)
\(\alpha(1.9) = 8\)
\(\alp…
Recursion and Summation Functions
- 1 Recursion Notation & Summation Function
- 2 Review of my Basic Notation
- 3 Recursion Notation
- 4 Summation Function
- 5 Further References
I use short hand notation for recursion of nested functions. They are a further development of notation I use that is not in common use.
Here is a summary review of my notation:
Decremented Function \(C\) is short-hand notation. For any arbitrary function:
\(M^{c + 1}(n)\) then \(C = M^{c}(n)\)
e.g.
\(M^{c + 1}(n) = M(C) = M(M^c(n))\)
Parameter Subscript Brackets is shorthand for functions with multiple parameters:
\(M(x,0_{[2]}) = M(x,0,0)\)
\(M(x,y_{[2]}) = M(x,y_1,y_2)\)
\(M(x,0_{[2]},y_{[3]},z) = M(x,0,0,y_1,y_2,y_3,z)\)
Leading Zeros Assumption applies to any function I define which accepts a variable number of input parame…
Alpha Spreadsheet q3.0
- 1 Alpha function code (Spreadsheet) version 3.0
- 2 Javascript code in Google Sheets
- 3 DRAFT Version 3.0 Examples
- 4 Code changes (in this version)
- 5 Recursion & Summation Functions
- 6 Further References
Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.
You are free to use and copy the code as you like. Version 3.0 of the Javascript code in Google Sheets is available here:
Alpha Function Spreadsheet
This replaces the Version 2.0 spreadsheet.
Some examples taken from the spreadsheet.
\(\alpha(2) = Q(1,2) = 5\)
\(\alpha(2.75) = Q^{2}(1,2_*) = 11\)
\(\alpha(3.1) = Q^{Q(2)}(1,2_*) = 23\)
\(\alpha(3.61) = Q^{Q^{2}(2)}(1,2_*) = 47\)
\(\alpha(4.29) = Q(t_0(0),2) = 95\)
\(\alpha(4.446) = Q(Q^{t_0(0)}(t_0(0)),2)\)
\(\alpha(4.60…
Alpha Function Code q2.0
- 1 Alpha Function Code (Quantum Function) version 2.0
- 2 Javascript code in Google Sheets
- 3 Version 2.0 Examples
- 4 Code changes (in this version)
- 5 Next Version
- 6 Further References
Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.
You are free to use and copy the code as you like. Version 2.0 of the Javascript code in Google Sheets is available here:
Alpha Function Javascript
This version replaces my previous Version 1.0 spreadsheet, but all versions are still available online.
Some examples taken from the spreadsheet.
\(\alpha(2) = Q(1,2) = 5\)
\(\alpha(2.75) = Q^{2}(1,2_*) = 11\)
\(\alpha(3.1) = Q^{Q(2)}(1,2_*) = 23\)
\(\alpha(3.61) = Q^{Q^{2}(2)}(1,2_*) = 47\)
\(\alpha(4.29) = Q(t_0(0),2) = 95\)
\(\alpha(5.8721)…
Alpha Function Code q1.0
- 1 Alpha Function Code (Quantum Function) version 1.0
- 2 Javascript code in Google Sheets
- 3 Version 1.0 Examples
- 4 Errors in the code
- 5 Further References
Javascript code for my Alpha Function based on my Quantum Function is available in Google Sheets.
You are free to use and copy the code as you like. Version 1.0 of the Javascript code in Google Sheets is available here:
Alpha Function Javascript
Some examples taken from the spreadsheet.
\(\alpha(0) = 0\)
\(\alpha(1) = 1\)
\(\alpha(1.375) = 2\)
\(\alpha(1.5) = Q(2) = 3\)
\(\alpha(2) = Q(1,2) = 5\)
\(\alpha(3.01) = Q^{Q^{2}(2)}(Q^{2}(1,2_*)) = Q^{4}(Q^{2}(1,2_*))\)
\(\alpha(4.286) = Q(t_0(0),2)\)
\(\alpha(4.3582) = Q^{Q^{Q^{2}(2)}(1,2_*)}(t_0(0),2_*)\)
\(\alpha(4.3625) = Q(Q(t_0(0)),2)\)
\(\alpha(4.44) = Q(Q^{t_0(…