Per Wikipedia, the music for the film was written by Richard Adler and Jerry Ross.
Richard Adler (August 3, 1921 – June 21, 2012) was an American lyricist, writer, composer and producer of several Broadway shows. .... Adler staged and produced several shows for U.S. presidents; the most notable of these was a 1962 Madison Square Garden birthday celebration for John F. Kennedy that included Marilyn Monroe singing a version of Happy Birthday to the president in her trademark breathy voice. .... He was a Democrat and, along with Democratic National Committee (DNC) Chairman John Bailey, Lena Horne, Carol Lawrence, Sidney Salomon, Vice-Chairwoman of the DNC Margaret B. Price, and Secretary of the DNC Dorothy Vredenburgh Bush, visited John F. Kennedy at The White House on November 20, 1963, two days prior to his assassination.
Jerry Ross (born Jerold Rosenberg; March 9, 1926 – November 11, 1955) was an American lyricist and composer whose works with Richard Adler for the musical theater include The Pajama Game and Damn Yankees, winners of Tony Awards in 1955 and 1956, respectively, in both the "Best Musical" and "Best Composer and Lyricist" categories. .... Jerry Ross died on November 11, 1955, at the age of 29, from complications related to the lung disease bronchiectasis. In his short life Ross was extremely productive; he wrote, alone or in collaboration, more than 250 songs in addition to his theatre work.
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