Collectively, of course, Frankie, Dean and Sammy were the leaders of the Rat Pack (the other members were Peter Lawford and Joey Bishop) who together graced stages and film sets.
They are all dead now, but their names and music live on.
The new show, which is performing twice at the King's Theatre today, is called The Rat Pack Vegas Spectacular Show, and features some of the best swing music ever made: Come Fly With Me, Under My Skin, Mr Bojangles, The Lady Is A Tramp, That's Amore, Mack The Knife, and more, all with a live orchestra and showgirls.
Wayne Kennedy plays Dean Martin. One recent review said of him: "Kennedy, bearing not the slightest resemblance to Dean Martin gives a remarkable impersonation of the star".
Wayne – who stars alongside Roman Marek as Sinatra and James Jnr as Sammy Davis – says: "I came from rock 'n' roll to theatre. I got to a stage in my career where I wondered what would suit the latter stages, and I decided that Dean Martin's solo voice was good for me. There was no Michael Jackson in my case! Dean's lower register was very good me for me.
"I spent 25 years commuting backwards and forwards from America and like to think I became very knowledgeable on all forms of American music, particularly the music from the 1940s to the end of the 1960s.
"It has worked well. The show has become a major worldwide production that employs 26 people, and the road to it has been quite incredible."
It helps, of course, that younger generations are discovering Rat Pack-era music for themselves.
Despite the songs' age – Sinatra's Come Fly With Me, for example, was written in 1957, while Martin's classic, That's Amore, dates from 1952 – they continue to hold their appeal. The same goes, of course, for Rodgers and Hart's The Lady is a Tramp, first published in 1937.
"That style of music never goes away," says Wayne. "It's timeless."
The same goes for Dean Martin who, even now, 18 years after his death, stands for a kind of effortless cool.
In the words of Playboy magazine, he was "the coolest man who ever lived." Elvis Presley adored him, too.
Martin started out delivering bootleg alcohol, then worked as a blackjack dealer, toiled in a steel mill and was even, for a while, a talented boxer.
Eventually, he landed his first singing engagements. He was a great success in his original partnership with comedian Jerry Lewis, and more so when he joined Sinatra & co in the Rat Pack.
He was renowned as the joker in the Pack, though, according to his website, he always insisted his cocktail-swilling persona was, by and large, a pose. "Basically, when I'm playing Dean, I'm playing the fool," is how Wayne puts it.
"But people forget that, amidst all the comedy, he was a great singer. No-one hits the low notes like Dean Martin. He was a very talented individual."
WAYNE is too young to have seen the Rat Pack in action. After all, they finished in 1966.
But his enthusiasm for his own show is, of course, undimmed.
"It's the real deal, as I like to say. It's totally live. We've got a touch of glamour with the Las Vegas showgirls, too, who do something like 13 clothes changes.
"The show's in its 11th year now and we always try to move forward. But certain songs are always guaranteed to appear."
Also guaranteed is a genuinely enthusiastic audience reception.
"Scottish audiences are always amazing. We love playing gigs in Hamilton and Motherwell, and this is our first time at the King's. We're looking forward to it so much."
n The Rat Pack Vegas Spectacular Show, King's Theatre, Bath Street. 3pm, 7.30pm. Tickets (£17-£21) from 0844 871 7648, or www.atgtickets.com