In the real world there are many applications that find the Bell distribution to be a useful and relevant model. One of these is the normal distribution. In this paper, we develop a new subclass of analytic bi-univalent functions by making use of the Bell distribution as a building block. These functions involve the Gegenbauer polynomials, and we use them to establish our new subclass. In this study, we solve the Fekete–Szegö functional problem and analyse various different estimates of the Maclaurin coefficients $\left|D_2\right|$ and $\left|D_3\right|$ for functions that belong to the built class.

Shakespeare portrays his protagonist in Macbeth as haunted by future memory. The blueprints of the future of Macbeth are provided by Supernatural aids. These equivocal blueprints breed the protagonist's prospective memory. However, the equivocation embedded in them leads to his confusion and the confusion of the whole country. In Ingvar (1985), who coined the expression "future memory," in neuropsychology, the concept is guided by past experience and mental imagination. In contrast, prospective memory of the protagonist is dictated by the supra-terrestrial agency of the three witches who take us off-guard at the outset of the play, and surprise Macbeth and Banquo in Act 1, Scene 3 and later in Scene of Act IV. The study hopes to analyze Ingvar's concept of future memory in neuropsychology and Shakespeare's version of the concept. It also hopes to demonstrate that the vision of the Elizabethan bard was not informed by empirical studies of the brain, but by the cultural concepts of his Age that used to give credibility to magic, demonology, fairies, and supernatural intervention in terrestrial life and time.