Hand gesture for Goddess Saraswati
Goddess Saraswati is considered the goddess of knowledge and speech. She is usually seen in white garments and fair in complexion. She is seated on a lotus. She has for arms holding the Veena (A string instrument), the rosary, and the vedas. The Veena represents her perfection on all arts. The Veena points the collective sound of all our thoughts and actions as it manifest in the universe a music. The rosary represents the power of meditation. The vedas are her command over science. Her vehicle is a divine swan (hamsa). Hence she is also called Hamsavahini. And She is the consort of God Brahma.
with reference to dance, Abhinayadarpanam states
suci krute dakshinecha vame chasamkrutau chamsamakrutau
kapittyakepey bhaatayaha kara syaditi sammattaha
Devi Saraswati is represented by holding suchi hasta in the right hand near the chest and the left hand in kapitta hasta raised above shoulder level