Perhaps some day we'll have audio of these 3 mantras associated with the mean time, here's how they are written. They are all in Sanskrit. [Update: there is now a recording of the Prajnaparamita invocation, Click "Listen" below.]

1) Prajnaparamita's Mantra

Her mantra--oṃ āḥ dhīḥ hūṃ svāhā--is all seed syllables, not 'regular words' with meaning, so not translatable. Here is some more info about this mantra and the seed syllable dhih from Visible Mantra.

Here is the Devangari script: 

oṃ āḥ dhīḥ hūṃ svā hā

2) The Heart Sutra mantra

The Heart Sutra mantra--gate gate pāragate pārasaṃgate bodhi svāha--comes at the end of the Heart Sutra. It is not usually translated into English.
gate gate pāragate pārasaṃgate bodhi svāha
(graphic from Conze--'Om' in the middle)

Translations of the Heart Sutra mantra

Edward Conze:
Gone, gone, gone beyond, gone altogether beyond, O what an awakening, all hail!

Thich Naht Hanh:
Gone, gone, gone all the way over, everyone gone to the other shore, enlightenment, svaha!

14th Dalai Lama:
Go, go, go beyond, go thoroughly beyond, and establish yourself in enlightenment.

Norman Fischer:
Gone, gone, utterly gone, awakening…wow!

3) Invocation to Prajnaparamita

This is the first line of the Heart Sutra in Sanskrit, which Conze translates as "Om Homage to the Perfection of Wisdom the Lovely, the Holy!"

oṃ namo bhagavatyai āryaprajñāpāramitāyai  (Listen.)

(More info about this mantra from Visible Mantra.)