Definitive biography of Wodehouse; P. G. Wodehouse: A Biography, by Frances Donaldson. New York: Alfred A. Knopf. 369 pp. $18.50.

''What luck . . . to have found Wodehouse at the age of seventy,'' writes Frances Donaldson. Mrs. Donaldson, who had known and loved the Wodehouse family since her childhood, only recently developed a taste for Wodehouse's writing.

Best known for her biography of Edward VIII (which was the basis for Masterpiece Theater's ''Edward and Mrs. Simpson''), Mrs. Donaldson takes aim, in her latest book, at a definitive biography of P. G. Wodehouse, that prince of hilarity. Wodehouse, who is admired as much for the clarity and brilliance of his style as for his wit, produced more than 90 books of farce, and was co-author and lyricist for 18 musical comedies.

Fellow Wodehouse fans will want to read this book, because we all want to know as much as possible about those we love. Donaldson's book is comprehensive; it's doubtful that new information about Wodehouse's life will emerge which would necessitate a major new biography.

But those searching for an introduction, those wishing to be taken by the hand and given a guided tour, to be shown the wonders of Wodehouse, may well be disappointed. Had I been a newcomer to the world of Wodehouse, I don't think the book would have made me want to read him, and he certainly merits that.

Mrs. Donaldson takes a searching look at Wodehouse's world through a lens colored (and occasionally distorted) by family friendships. Wodehouse himself seems, at times, to have been stretched out on the Procrustean bed of psychology , his personality lopped off at either end, the better to fit the interpretation.

Donaldson makes a serious effort to separate fact from rumor and badinage - no easy task. A reader looking for the truth must cast a dubious eye even on statements which are direct quotes from Wodehouse himself. According to Guy Bolton, Wodehouse's best friend and Broadway collaborator, the painfully shy Wodehouse had such an aversion to contretemps that he once told Bolton, ''Let's agree that if someone says an unkind thing about the other, don't argue, just agree - adding details.''

Donaldson, with access to letters and information previously unavailable, has been able to take a clear-eyed look at controversial portions of Wodehouse's life. It helps, too, that she lived through so many of the events she recounts.

She is at her best in her portrayal of the war years and the social milieu of the early part of this century. Complete transcripts of the notorious German broadcasts during World War II (for which Wodehouse was accused, and only recently vindicated, of treason) are included as an appendix.We emerge from the chapters dealing with these broadcasts with an understanding of how Wodehouse could have been so innocent and so foolish, and with a sense that Donaldson has been both compassionate and objective.

But all too often she sacrifices this objectivity to sentiment. Her portrayal of Wodehouse's adopted daughter, Leonora (Snorky), who was also Donaldson's close friend, is so charged with affection that she seems too perfect to be human. Donaldson's grief over Snorky's death is palpable throughout the book.

Wodehouse's wife, Ethel, conversely, is painted in somewhat unflattering terms, without enough detail to let us know if the portrait is lifelike.

Donaldson's style, often elegant but occasionally pedantic, is somewhat lacking in zest and vitality. Her handling of detail is sometimes clumsy and repetitious. There are too many protests of enthusiasm for Wodehouse's work and too few inspired quotations.

Part of the problem may be that Wodehouse's life was so much less interesting than his writing. As his almost incredible output proves, his writing was his life.

But his other biographers, notably Richard Usborne and David Jasen, have managed to capture more of Wodehouse's own flavor. Usborne, in ''Wodehouse at Work to the End,'' may have had an easier time because he concentrated primarily upon the Wodehouse work.

I came away wishing this new book had been written with more of the spirit of Wodehouse. In a word, more show, less tell.