This raga has become famous because of the Tyagaraja kriti "Bantureethi Kolu". This is a janya ragam of Neethimathi which is the 60th melakarta ragam. Now, before we proceed further with Hamsanadham, let's understand what is melakarta ragam and what is janya ragam.
Melakarta is a collection of fundamental ragas in Carnatic music. Melakarta ragas are parent ragas (hence known as janaka ragas) from which other ragas may be generated.There are 72 melakarta ragams in carnatic music. A melakarta raga is sometimes referred as mela, karta or sampoorna as well.There are some conditions on the basis of which a raga is classified under the title melakarta. Let's not discuss about it at this point of time.
In Carnatic music, Janya(meaning derived from) Ragas are the Ragas derived from the 72 melakarta (fundamental) ragas.
As always, Ilayaraja has used Hamsanadham more than any other music director. Interestingly, Ilayaraja had no formal training in carnatic music. "Thendral vandhu ennai thodum" from Thendrale Ennai Thodhu, "Om Namaha" from Idhayathai Thirudathe, "Sorgame Endralum" from Ooru vittu ooru vandhu, "Isaiyil Thodangudhamma Inba Nadagame" from Hey Ram are all composed in Hamsanadham.
I am not aware of any Hamsanadham number composed by ARR but "Enakena Yerkanave" from Paarthen Rasithen is composed in Hamsanadham by Bharathwaj.