(HP35S) Lambert W Function
|
08-19-2024, 10:49 AM
(This post was last modified: 08-20-2024 11:17 AM by Roberto Volpi.)
Post: #1
|
|||
|
|||
(HP35S) Lambert W Function
Hi all
The following program, using the native solver, can compute numerical values of the Lambert W Function, and also those resulting by substituting e with an arbitrary positive constant “a”. … The Lambert W Function can be defined as the inverse of y=xe^x. As the implicit form x=ye^y is not very useful onto itself, we can use the native solver of our beloved HP35S to obtain a numerical solution, just by using a short program and an even shorter subroutine. The program is: LBL L STO X FN=W SOLVE W RCL X x<>y RTN The subroutine is: LBL W RCL W e^x RCL xW RCL -X RTN INSTRUCTIONS: - Input value, whose L(W) we wish to calculate (it will be stored STO X) - XEQ L Our HP35S will display: - X value on stack y - Its L(W) on stack x A FUNCTION WITH (STILL?) NO NAME. Instead of e, we can use an arbitrary positive constant, which we shall name “a”, and we obtain a more general form of the Lambert W Function, which sometimes can be useful to solve quickly some equations, without manipulating them to obtain a xe^x form. Just let a^x = e^(x ln a) and that’s it. Now the W subroutine will be as follows: LBL W RCL A RCL W y^x RCL xW RCL -X RTN INSTRUCTIONS: - Input “a” value, and press STO A - Input value, whose L(W) we wish to calculate (it will be stored STO X) - XEQ L Our HP35S will display: - X value on stack y - Numerical result of that unnamed funtion on stack x I have found no written reference of that new function. My wife, with her spiffing sense of humour, told me that I can baptize it with my name… I see that very few programs for the HP35S have been submitted in recent times, and that is unfortunate, because this calculator can be still a valuable tool for both professionals and students. Put a calculator into your life! |
|||
« Next Oldest | Next Newest »
|
Messages In This Thread |
(HP35S) Lambert W Function - Roberto Volpi - 08-19-2024 10:49 AM
RE: (HP35S) Lambert W Function - PedroLeiva - 08-19-2024, 12:14 PM
RE: (HP35S) Lambert W Function - jdebord - 08-20-2024, 06:23 AM
RE: (HP35S) Lambert W Function - Roberto Volpi - 08-20-2024, 09:49 AM
RE: (HP35S) Lambert W Function - PedroLeiva - 08-20-2024, 11:00 AM
|
User(s) browsing this thread: 2 Guest(s)