Mr Davis moved to Honolulu from Chicago in 1948 with his second wife Helen Canfield, a white socialite, at the suggestion of his friend the actor Paul Robeson, who advised them that there would be more tolerance of a mixed race couple in Hawaii than on the American mainland.
A bohemian libertine who drank heavily and loved jazz, he became friends with Stanley Dunham, Mr Obama’s maternal grandfather in the 1960s. Mr Davis died in 1987 at the age of 81, five years before Mr Dunham.
“He knew Stan real well,” said Dawna Weatherly-Williams, a close friend of Mr Davis “They’d play Scrabble and drink and crack jokes and crack jokes and argue. Frank always won and he was always very braggadocio about it too. It was all jocular. They didn’t get polluted drunk. And Frank never really did drugs, though he and Stan would smoke pot together.”
While his mother was in Indonesia during part of his teenage years, Mr Obama lived with his white grandparents. Mrs Weatherly-Williams said that the poet was first introduced to the future Democratic presidential candidate in 1970 at the age of 10.
“Stan had been promising to bring Barry by because we all had that in common - Frank’s kids were half-white, Stan’s grandson was half-black and my son was half-black. We all had that in common and we all really enjoyed it. We got a real kick out of reality.”
Maya Soetoro-Ng, Obama's half-sister, told the Associated Press recently that her grandfather had seen Mr Davis was “a point of connection, a bridge if you will, to the larger African-American experience for my brother".
In his memoir, Mr Obama recounts how he visited Mr Davis on several occasions, apparently at junctures when he was grappling with racial issues, to seek his counsel. At one point in 1979 Mr Davis described university as “an advanced degree in compromise” that was designed to keep blacks in their place.
Mr Obama quoted him as saying: “Leaving your race at the door. Leaving your people behind. Understand something, boy. You’re not going to college to get educated. You’re going there to get trained.”
He added that “they’ll tank on your chain and let you know that you may be a well-trained, well-paid nigger, but you’re a nigger just the same.”
It has also been established that Mr Davis, who divorced in 1970, was the author of a hard-core pornographic autobiography published in San Diego in 1968 by Greenleaf Classics under the pseudonym Bob Greene.
In a surviving portion of an autobiographical manuscript, Mr Davis confirms that he was the author of Sex Rebel: Black after a reader had noticed the “similarities in style and phraseology” between the pornographic work and his poetry.
“I could not then truthfully deny that this book, which came out in 1968 as a Greenleaf Classic, was mine.” In the introduction to Sex Rebel, Mr Davis (writing as Greene) explains that although he has “changed names and identities…all incidents I have described have been taken from actual experiences”.
He stated that “under certain circumstances I am bisexual” and that he was “ a voyeur and an exhibitionist” who was “occasionally mildly interested in sado-masochism”, adding: “I have often wished I had two penises to enjoy simultaneously the double – but different – sensations of oral and genital copulation.”
The book, which closely tracks Mr Davis’s life in Chicago and Hawaii and the fact that his first wife was black and his second white, describes in lurid detail a series of shockingly sordid sexual encounters, often involving group sex.
One chapter concerns the seduction by Mr Davis and his first wife of a 13-year-old girl called Anne. Mr Davis wrote that it was the girl who had suggested he had sex with her. “I’m not one to go in for Lolitas. Usually I’d rather not bed a babe under 20.
“But there are exceptions. I didn’t want to disappoint the trusting child. At her still-impressionistic age, a rejection might be traumatic, could even cripple her sexually for life.”
He then described how he and his wife would have sex with the girl. “Anne came up many times the next several weeks, her aunt thinking she was in good hands. Actually she was.
“She obtained a course in practical sex from experienced and considerate practitioners rather than from ignorant insensitive neophytes….I think we did her a favour, although the pleasure was mutual.”
On other occasions, Mr Davis would cruise in Hawaii parks looking for couples or female tourists to have sex with. He derived sexual gratification from bondage, simulated rape and being flogged and urinated on.
He boasted that “the number of white babes interested in at least one meeting with a Negro male has been far more than I can handle” and wished “America were as civilised as, say, Scandinavia”. He concluded: “I regret none of my experiences or unusual appetites; for me they are normal.”
According to Mrs Weatherly-Williams, Mr Davis lost touch with Mr Dunham some time in the 1980s. John Edgar Tidwell, who wrote the introduction to Davis's memoir and edited a collection of his work, said that there was no mention of Mr Dunham or Mr Obama in any of Mr Davis’s papers.