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Bharata Natyam 
Elizabeth Kelly 

Anjali: If the palms of both hands are joined forming the pataka hasta, it is called Anjali hasta.

This is applied to show respect, salutation and regards to Maheśa (Lord Siva), to preceptor, teacher, etc and washing.

Kapota: When forming sarpasīrsa hasta with both hands with rubbing of fingers kapota hasta is formed.

It shows salutation, giving rewards to the guides, protection, feeling cold etc.

Karkaṭa: When fingers of both hands of padmakośa formation are interlocked, it is karkata.

It shows the message of limbs and holding the śankha (shell).

Research 
Elizabeth Kelly 

Svastika: Both hands are kept upwards in the arala hasta touching with each hand the side of the other hand and the wrists are joined, it is svastika

Bringing any body after binding closely is indicated by this hasta.

Bharata Natyam 
Elizabeth Kelly 

Dolahasta: If both hands are spread down with pataka hasta it is dola hasta

This should be used in sorrow intoxication, unconciousness, illness and confusion.

Bharata Natyam 
Elizabeth Kelly 

Puṣpapuṭa: In sarpasīrsaka hasta if the little fingers are put on the sides of both hands it is puṣpapuṭa.

This hasta is applicable in salutation with flowers and water.

Research 
Elizabeth Kelly 

Utsanga: When two arala hastas with opposite sides are joined and kept higher up, it is called utsanga.

It shows the separation of lover, and playing ball, etc.

Research 
Elizabeth Kelly 

Kaṭaka vardhamāna: when the kaṭaka formation is put upon the kaṭakahasta it is kaṭaka vardhamāna.

(Edit note - this real is a self-referential translation.  The image provided is a best guess)

It is applied to show the holding of weapons, spear, etc. and the playing of kahala (a large drum).

Avahittha: If both hands forming śukatunda are held in front of the chest and slowly curved downward is avahittha.

It shows weakness and anxiety.

Gajadanta : If sarpasīrsaka hasta is formed no etalies (???) in both hands are spread out in front and kept a little upward it is gajadanta.

It is used to indicate the bearing of heavy burdens big stone and child etc.

Naiṣada: If the right hand in the form of musti hasta is kept on the middle of the left elbow and the upper part of the hand on the right, it is nisada.

It is used to show bravery or pride.

Makara: If the pataka hasta formed in both hands are kept upon the both wrists, facing upward, it is makara.

This is applied to show lion, śārdula (fierce animal) and crocodile.

Vardvmāna: With the kapittha hands if the mukula hasta is tried to form, it is vardhamāna

It shows collection, brevity and satya vākyam (veracity).