Liddell-Scott-Jones

αὐχέω (aucheō) to boast ^G:V

αὐχέω,

chiefly present and imperfect ηὔχουν, future αὐχήσω[Refs 5th c.BC+]aorist ηὔχησα[Refs 2nd c.AD+]: (αὔχη):—boast, plume oneself, ἐπί τινι on a thing, [Refs 5th c.BC+]: with neuter adjective, τοσοῦτον αὐχεῖν[NT+5th c.BC+]: with accusative objecti, to boast of, ἀστέρας[Refs]

__II with accusative et infinitive, boast or declare loudly that.., αὐχέοντες κάλλιστα τιθέναι ἀγῶνα[Refs 5th c.BC+]; σώσειν (σῶσαι codices) [Refs 5th c.BC+] boast (that I hold her), [Refs]
__II.2 with infinitive future, say confidently, to be proudly confident that, αὐχῶ γὰρ αὐχῶ τήνδε δωρεὰν ἐμοὶ δώσειν Δί᾽[Refs 5th c.BC+] I never thought that.., [Refs 5th c.BC+]
__III middle, αὐχήσασθαι· καυχήσασθαι, [Refs 5th c.BC+]; rare in Comedy texts and Prose.

_{LSJ Scripture Refs: Jas.3.5}