Dr. Wilf wrote six books and more than 160 research articles. From the 1950s, he was a pioneer in the mathematical programming of early computers, and in 1967, he and Anthony Ralston published the book Mathematical Methods for Digital Computers.
Dr. Wilf and Zeilberger, a professor at Rutgers University, developed the Wilf-Zeilberger pair, a theory used in computer algebra software. In 1998, the American Mathematical Society awarded them the Steele Prize.
Joan Hutchinson, a former doctoral student of Dr. Wilf's, said that he was an advocate of open electronic publishing of books and journals and that many of his books are available for free download on his Web page.
He cofounded the Journal of Algorithms in 1980 and the Electronic Journal of Combinatories in 1994. From 1987 to 1992, he was editor in chief of the American Mathematical Monthly.
Dr. Wilf lectured at colleges, universities, and mathematics conferences throughout the world. Even after retiring from Penn in 2008, he continued to do research and attend conferences, his wife said.
Dr. Wilf grew up in Wynnefield and graduated from Central High School. He earned a bachelor's degree from the Massachusetts Institute of Technology in 1952 and a doctorate in mathematics from Columbia University in 1958. He was assistant professor of mathematics at the University of Illinois before joining the Penn faculty.
He and his future wife met when they were college freshmen; she attended Wellesley. They married in 1952.
His wit, his wife said, shone through in some of his whimsical research-paper titles, such as "The Snake Oil Method for Proving Combinatorial Methods."
From 1982 to 2002, Dr. Wilf flew a single-engine plane as a hobby. In an essay about the experience, he wrote that although the national average for getting a pilot's license was 70 hours of instruction, he made his first solo flight after just 40 hours. "The only problem was I didn't know how to keep the plane going straight down the runway after landing."
In their vintage 1965 Cessna, he and his wife flew to Mexico, Florida, the Bahamas, Alaska, and western and eastern Canada. Sometimes on short trips, he wrote, their dog, Charlie, was copilot, "resting her nose on my right shoulder while I was trying to concentrate on flying the aircraft."
Dr. Wilf battled ALS, a progressive neuromuscular disorder also known as Lou Gehrig's disease, for a year but "was never cranky and bore it with fortitude," his wife said.
In addition to his wife, Dr. Wilf is survived by a daughter, Susan; sons David and Peter; and six grandchildren.
A memorial service will be held at 3 p.m. Sunday, Jan. 15, at Temple Beth Hillel-Beth El, 1001 Remington Rd., Wynnewood.
Donations may be made to the Herbert S. Wilf Award Fund, Department of Mathematics, University of Pennsylvania, 209 33d St., Philadelphia 19104.
Contact staff writer Sally A. Downey at 215-854-2913 or email@example.com.