Check this link out: 

http://colormine.org/color-converter

A good book is Mark Fairchild, Color Apperance Models, 3rd Ed.

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1119967031.html

On-line calculator, math formula overview, links:

http://www.brucelindbloom.com/

Dear Professors, 

Kindly thanks for your helpful replies,

Best Regards,

Farshid Keivanian

hi

http://uk.mathworks.com/help/images/ref/lab2rgb.html

even you can have all kind of image conversion here at the bottom of the page:

http://uk.mathworks.com/help/images/functionlist.html

interested subject

interested details

good information

You can check the following links:

http://docs-hoffmann.de/cielab03022003.pdf

http://www.compression.ru/download/articles/color_space/ch03.pdf

Kindly thanks dear researchers, Hssam, Noori, Mousavi, Volker, Jan, and Béatrice Marianne.

here is a link to some free software that does these types of conversions and more:

https://www.osram.us/cb/tools-and-resources/applications/led-colorcalculator/index.jsp

This is app and free on line converter:

https://nixsensor.com/free-color-converter/

For my job, I've written a Macro that does exactly that. Currently, it uses the variables for a specific illuminant (which I intend on expanding), but automatically colors the cells next to the LAB values (which I intend on changing as well) with the corresponding RGB colors. If still interested, please take up contact with me.

Edit: Here is the link to my GitHub with the UserForm:

https://github.com/Mister-Dinky/LAB-to-RGB: An Excel UserForm to convert CIELAB values to RGB