Longing

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Old English langian ‘grow long, prolong’, also ‘dwell in thought, yearn’, of Germanic origin; related to Dutch langen ‘present, offer’ and German langen ‘reach, extend’.

wiktionary

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From Middle English longynge, langynge, langand, from Old English langiende, from Proto-Germanic *langōndz, present participle of Proto-Germanic *langōną(“to desire, long for”), equivalent to long +‎ -ing(present participle ending).

From Middle English longinge, langynge, from Old English longung, langung(“longing, desire”), from Proto-Germanic *langungō, gerund of Proto-Germanic *langōną(“to desire, long for”), equivalent to long +‎ -ing(gerund ending).

etymonline

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longing (n.)

"yearning, eager desire, craving," Old English langung "longing, weariness, sadness, dejection," verbal noun from long (v.).

2. Specifically, in pathol., one of the peculiar and often whimsical desires experienced by pregnant women. [Century Dictionary, 1899]

longing (adj.)

early 15c. (implied in longingly), present-participle adjective from long (v.).