Agajanana Padmakam

अगजानन-पद्माकं गजाननम्-अहर्निशम्।
अनेकदंतं भक्तानाम् एकदन्तम्-उपास्महे ॥१॥

agajānana-padmākaṃ gajānanam-aharniśam.
anekadaṃtaṃ bhaktānām ekadantam-upāsmahe ..1..

We meditate day and night on the one-tusked one who is the sun for the lotus in the form of the face of Pārvatī, the one with the elephant face and the one who is the giver of all desired ends to his devotees.
(Or)
As the rays from the lotus-face of Gauri (Devi Parvati) is always on her beloved son Gajanana (Who has the face of an elephant), similarly, the Grace of Sri Ganesha is always on his devotees; granting their many prayers; the devotees who with deep devotion worship the ekadanta (one with a single tusk).

Description

Agajanana Padmarkam is a well-known sloka in praise of Lord Ganesha, the removal of all obstacles. The shloka says that Lord Ganesha is the giver of all (anekadam) to devotees who sincerely invoke him.

Excerpt from the book ‘Prayer Guide’ by Swami Dayananda Saraswati
Gajananam ekadantam aharnisam upasmahe. Gaja is elephant and anana means face. Gajanana is one who has the face of an elephant. Ekadanta is the one who has only one danta, tusk. Upasmahe means we meditate upon and aharnisam means day and night. We meditate day and night upon that one who has the face of an elephant, and who has one tusk.

Agajanana-padmarkam is a compound word. That which is born is jah, jayate iti jah. Gah means that which goes, gacchati iti gah. Agah means that which does not move, na gacchati iti agah, parvata, mountain. The king of the mountain is parvata-raja. Agat jayate, then, is the one who is born of aga, the mountain king. This is Goddess Parvati. Parvati is called Agaja, Girija. In this context agajananam is agajayah ananam, the face of Goddess Parvati. This face of Parvati is likened to the lotus, padma, agajananam eva padmam.

For a lotus to bloom, the presence of the sun is required. While the water-lily blooms in the wake of moon at night, the water-lotus blooms only when the sun is up. Arka means sun. So too Parvati’s lotus like face requires a sun to bloom, and this is Lord Ganesa. He is the one who is the sun, as it were, for the lotus that is the face of Goddess Parvati. When she sees Lord Ganesa, she is so happy that her face blossoms. Lord Ganesa is himself gajanana, who has the face of an elephant which is a symbol for all wisdom and all power.

What is anekadantam? It is anekadam tam. The one who gives is dah, dadati iti dah. The one who gives ekam, one thing, is called ekadah, ekam dadati iti ekadah. Lord Ganesa is not the giver of only one thing. He is anekadah, the giver of all that you want; in the second case-ending, it is anekadam. He gives aneka: dharma, artha, kama, and moksha. You can get everything by his grace. Tam means him. Anekadam tam means unto that Lord whose grace will help you achieve everything. For whom is he anekadah?

Bhaktanam, for his devotees, those who invoke him. We meditate upon this Lord Ganesa.