The exhibition, which comprises about 50 works by the artist, also recognises Hotere's 80th birthday on August 11.
The selection spans more than four decades of Hotere's career and draws on several different Dunedin collections, including the Hocken, the Hotere Foundation Trust, Hotere's own collection and other private collections, Hocken pictorial collections curator Natalie Poland says.
"We wanted to do something to commemorate his birthday because of his ties with the University of Otago. He was one of the first Frances Hodgkins Fellows (1969) and also received an honorary doctorate from the university in 1994."
The concepts of zero and infinity, which refer to nothing and boundlessness or eternity, are manifest through a series of visual signs that appear in Hotere's work, including the colour black, the circle and the window frame.
"I was intrigued by how the notion of infinity is conveyed through many of the characteristic aspects of Hotere's work - the blackness and the use of a window frame - yet the symbol itself only appears in a few works. This is a quieter aspect of his work that I had not previously noticed," Ms Poland says.
"The show's approach has also allowed us to include a work that he did recently, in 2005, based on the infinity symbol, the number 8 on its side. It is on stainless steel, which is another key character of his work, and is presented within the colonial sash window frame, which again is quite characteristic of his window works of the 1980s."
Ms Poland, who started preparations for the exhibition a year ago, admits it was difficult narrowing the selection, but believes "Zero to Infinity" covers milestones such as Hotere's Window series as well as less-celebrated material.
"We included a work from his Zero series in the 1960s, which is a series most people won't be familiar with. I guess unless you know his work really well, you wouldn't know from the title that it was a direct reference.
"I wanted something that represented each decade. I wanted some of what are termed his milestones, his signature series like the Black Windows and his Sangro series."(Begun in 1962, the Sangro series is a memorial to Hotere's brother, Jack; a member of the Maori Battalion, he is buried at the Sangro River War Cemetery in Italy.)"
We have some very large works in the exhibition. The Voyage is 3m high, just a single unstretched canvas; it is quite raw looking and, like a few of his works in the exhibition, incorporates words from Bill Manhire."
The Voyage (1975-76) is a "Song Cycle" banner, conceived to accompany a sound, movement and theatre performance, incorporating the Manhire poem of the same title.
The inclusion of the work in the exhibition is an acknowledgement of Hotere's friendships and collaborations with many of New Zealand's leading poets.
There are also works more political than poetic: anger over the proposed aluminium smelter at Aramoana is distilled in Black Window Port Chalmers (1982), a painting encased by a colonial sash window.
Another, an austere black painting simply titled Port Chalmers Painting No. 9 (1972), further references the place Hotere held dear since moving to Dunedin in 1969, Ms Poland says.
Hotere's works have often responded to current events, both local and international.
Le Pape est Mort was inspired by a newspaper headline announcing the deaths of two modern popes in 1978, while Hotere was studying in France; another, White Drip (2003), was Hotere's response to broadcaster Paul Holmes' "cheeky darky" comment of 2003.
A 2.7m-long piece of corrugated iron (now a signature material for Hotere) is painted in black with a drip of white paint extending nearly the full height of the work, with the reference to Holmes expressed through the stencilled type "To Mister Paul Holmes".
See it
"Ralph Hotere: Zero to Infinity" opens at the Hocken Gallery, Dunedin, on Saturday and runs until October 1.
Another event planned to coincide with Ralph Hotere's 80th birthday is the restoration of the Hotere artwork Rain (1979), owned by the University of Otago.
Rain comprises three 5m-high banners that incorporate the poem Rain by Hotere's long-time friend and the university's former Burns Fellow, the late Hone Tuwhare.
The banners were commissioned by the University of Otago in 1979, when the Hocken Library building, designed by Ted McCoy, was being built.
The banners hung in the foyer of that building, now known as the Richardson Building, for almost 30 years. They were removed in 2007 and have been in storage at the Hocken awaiting conservation.
The necessary restoration work, carried out by Auckland paintings conservator Lydia Gutierrez, will be completed this month, after which the banners will be re-hung at a location yet to be decided.
"We haven't decided where yet," Hocken pictorial collections curator Natalie Poland said.