The royal couple met during the 2000 Sydney Olympics
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Australia is to send a first edition of a classic children's book to Denmark's crown prince and his Australian-born wife on the birth of their child.
Prime Minister John Howard said the 1918 copy of Snugglepot and Cuddlepie was "an entirely appropriate Australian gift for this wonderful event".
Crown Prince Frederik and Crown Princess Mary announced the birth of their first child, a boy, on Saturday.
The child, born in Copenhagen, becomes second in line to the Danish throne.
He is expected to be named Christian, in line with royal tradition.
Tasmania tie
Snugglepot and Cuddlepie has been one of Australia's best-loved children's books for generations.
Written by May Gibbs at the end of World War I, it tells of the adventures of gumnut babies - imaginary characters who live in gumnuts - and their encounters with heroes and villains in bush world.
Mr Howard told reporters: "We congratulate Frederik and Mary on the safe arrival of their child, and the fulfilment of all new parents' wishes that mother and child are doing well."
Crown Princess Mary, 33, was born on the Australian island state of Tasmania.
Crown Prince Frederik met his future wife, the then Mary Donaldson, in a bar during the Sydney Olympics in 2000.
The couple married in a lavish ceremony in Copenhagen in May last year.
Speaking after his son's birth, Crown Prince Frederik said: "It is impossible to describe that feeling for me and my wife, who is doing fine."
He joked that he had assisted by cutting the umbilical cord.
"I was of great help if I can say it myself," he said.
The baby was born at 0157 on Saturday (2357 GMT Friday) at the Copenhagen University Hospital and weighed 3.5kg (7lbs 11 oz), the royal palace said.
The Danish royal family traces its roots back to Gorm the Old, a Viking king who died in 958.