Circular Waveguide || Further discussion and problem solving

In this video, further discussion on circular waveguide is done and cut-off frequency, loss are explained using example

[angelicadizon]

can you please answer me, how did you get the value of Beta? thank you

[dhin]

Please let me know how to find the Pnm (table). Please solve any one i.e., n=0, pn, 1 (from Kc or fc). Because I check some books no one says this is the formula to find the Pnm or P'nm.

[dhin]

And pls let me know what is the value of 'a' (for kc and fc)