Mustadrak al-Hakim — Hadith 2027

It is narrated from Sayyiduna Abu Umamah (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) said: "When the caller (the mu'adhdhin) calls the adhan, the gates of the heaven are opened and supplication is answered. So whoever is afflicted by some distress or hardship should wait for the mu'adhdhin('s adhan). Then when the mu'adhdhin says Allahu Akbar, he too should say it; when he bears witness, he too should bear witness; when he says 'Hayya 'ala al-salah' (Come to prayer), he too should say 'Hayya 'ala al-salah'; when he says 'Hayya 'ala al-falah' (Come to success), he too should say 'Hayya 'ala al-falah'. Then he should say: 'Allahumma Rabba hadhihi al-da'wati al-sadiqati al-mustajabi laha, da'wati al-haqqi wa kalimati al-taqwa, ahyina 'alayha, wa amitna 'alayha, wab'athna 'alayha, waj'alna min khiyari ahliha ahya'an wa amwata' (O Allah, Lord of this truthful call which is answered, the call of truth and the word of piety, keep us alive upon it, cause us to die upon it, raise us upon it (on the Day of Resurrection), and make us among the best of its people in both life and death). After that he should ask Allah for his need."
The chain of this hadith is sahih (authentic), but the two Shaykhs (Bukhari and Muslim) did not record it.