ありがたく

• 有り難く (with kanji)

Adverbial (-く form) of ありがたく or ありがたい • (arigataku)  (arigatai, "grateful, thankful; welcome"), from Old Japanese 有り難し (arigatasi).

Historically from 有り (ari), the continuative form of 有る (aru, “to exist, to be”) + 難し (katashi, “hard, difficult”), with rendaku.

• (Tokyo) ありがたく [àrígáꜜtàkù] (Nakadaka – [3])
• IPA^(key): [a̠ɾʲiɡa̠ta̠kɯ̟]

ありがたく • (arigataku) 

1. gratefully, thankfully, with gratitude

   彼(かれ)の助(じょ)言(げん)をありがたく受(う)け入(い)れた。

   Kare no jogen o arigataku ukeireta.

   I gratefully accepted his advice.

   ご好(こう)意(い)をありがたく頂(ちょう)戴(だい)します。

   Gokōi o arigataku chōdai shimasu.

   I will gratefully accept your kindness.

During the Muromachi period, the medial /k/ in adverbial forms dropped out, with -ku becoming -u. While most adverbs later reverted to -ku, this form persisted as -u in certain set expressions, eventually becoming ありがとう (arigatō), still used today as a common expression of thanks.

• ありがとう (arigatō, “thank you”)

• ありがたい (arigatai) – adjective
• ありがたみ (arigatami) – noun: thankfulness, appreciation
• ありがたがる (arigatagaru) – verb: to feel grateful
• ありがたさ (arigatasa) – noun: gratefulness