The issue of Persian influence in Bangla literature can be treated from 3 points of views: Use of Persian words in Bangla literature, translations of works from Persian poets and writers and influence of Persian writing, religion, society and philosophy in the works of Bengali poets and writers. This is such a vast topic that a number of books can be written about it. In this article, I will just cast some light about this topic based on the 3 categories I just mentioned. There has been some research about this theme in Bangla language but nothing substantial in English or in Persian (Farsi).
There is no accurate statistics of the number of Persian words in Bangla language. Estimates vary from 3000-8000 words. Some words are used in everyday language and most people even do not know that these words are foreign words. After the Muslim conquest of Bengal in 1204, for the next 2 centuries we hardly find any works written by Muslims in Bangla. Muslims writers were always divided in using Persian words from first. Some writers used a lot of Persian and Arabic words in their writings. Some writers have completely refrained from doing so. Many poets and writers have followed a middle ground by mainly using the religious words and very common words. The current trend is to use the every day used Persian words of Bangla language in literature. However, one thing should be noted here. Persian words have been used by both Hindu and Muslim poets and writers.
From first the Muslims writers and even some Hindu writers have either directly translated texts from Persian literature or wrote their own version of a popular story. Not only Persian texts on religion have been translated but romantic tales were very popular also. Leili Majnu, Yousuf Joleykha are among the popular Persian tales that have been either translated or retold by more than one poets in Bangla literature. Works of Hafiz, Omar Khyam, Jalaluddin Rumi, Ferdowsi have also been translated in Bangla.
Many poets in Bangla literature have been deeply influenced by Persian literature, philosophy and religion. The influence of Persian literature is clearly evident in the writings of two of the greatest figures of Bangla literature, Rabindranath Tagore and Kazi Nazrul Islam. Tagore was influenced by the mysticism of Hafiz. Tagore's father was a passionate admirer of the poems of Hafiz and in Taore's poetry is heavily domainted by love, beauty and mysticism- common themes in the poetry of Hafiz too. On the other hand, Kazi Nazrul Islam knew Persian very well and he was familiar with Persian literature perhaps more than any other writer in Bangla literature in 20th century. Kazi Nazrul Islam has used Persian words very skillfully and surpassed every poet before or after him in this matter.
Persian influence in Bangla literature has enriched Bangla literature a lot. It has added a new flavor to Bangla literature and has contributed a lot in its development.