Quoting Commentary for I Kings 18:37

עֲנֵ֤נִי יְהוָה֙ עֲנֵ֔נִי וְיֵֽדְעוּ֙ הָעָ֣ם הַזֶּ֔ה כִּֽי־אַתָּ֥ה יְהוָ֖ה הָאֱלֹהִ֑ים וְאַתָּ֛ה הֲסִבֹּ֥תָ אֶת־לִבָּ֖ם אֲחֹרַנִּֽית׃

Hear me, O LORD, hear me, that this people may know that Thou, LORD, art God, for Thou didst turn their heart backward.’

Radak

My God, my God, why hast Thou forsaken me? – (The address) in the singular refers to the people of Israel as a whole, for they were as one man in exile and of one mind. My God, my God: the repetition is after the manner of those who call out and cry, as: “Hear me, O Lord, hear me” (1 Kings 18:37); “Abraham, Abraham” (Gen. 22:11); “Moses, Moses” (Exod. 3:4). Israel says also אלי (my God or my Strength), meaning: Thou wast my Strength and my Rock before, and now, why hast Thou forsaken me?
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Rabbeinu Bahya

You will note that whereas Elijah offered up numerous prayers at Mount Carmel, G’d did not respond to him until after he had mentioned the dead. When he pleaded ענני ה’ ענני, “answer me O Lord, answer me,” nothing happened until he added the words ה’ אלו-הי אברהם יצחק וישראל, “Lord G’d of Avraham, Yitzchak and Israel, today let it be known that there is a G’d in Israel.” As soon as he had concluded this particular prayer, fire fell from heaven and consumed the burnt-offering as well as the firewood and the stones. [I find this Midrash difficult as in the text you will note that Elijah mentioned the patriarchs before pleading ענני ה’ ענני. We may have to assume that the previous prayers are simply not recorded in the text (Compare Kings I 18,36)]
Moses, likewise, remained on Mount Sinai for forty days to ask G’d’s mercy for His people for the sin of the golden calf and he was not answered until he mentioned the dead by saying: “remember Avraham, Yitzchak and Yaakov.” As soon as he did that, the Torah writes וינחם ה’ על הרעה אשר דבר לעשות לעמו “The Lord reconsidered the evil He had said to do to His people.” The whole episode helps us understand what Solomon referred to in Kohelet 4,2 when he said: “I praise the dead who are dead already.” He meant that such dead are even more effective in death than live and righteous people are while still alive. This is what the sages meant when they said that the righteous dead are greater in death than while they were still alive” (Chulin 7).
Another approach to this verse in Kohelet: Solomon meant that the dead who were righteous during their lives long ago were greater in their lifetime than the righteous of the present generation in their lifetime (Shabbat 30,1). The proof is that the decrees handed down from the times of Moses are still being observed (though Moses has been dead a long time), whereas the decrees issued by kings nowadays, kings who are alive, are frequently not being observed. Moses himself had introduced numerous תקנות, ordinances, over and above the explicit laws spelled out in the Torah. To name but one: when the Torah writes in Leviticus 23,44 וידבר משה את מועדי ה’ אל בני ישראל, “Moses stated the laws about the festivals of G’d to the Children of Israel,” the Talmud Megillah 32 explains that Moses instituted the rule that the laws about keeping these festivals have to be expounded publicly on that day or earlier. We find that Ezra also added new such ordinances which are still being observed in our time (compare Baba Kama 82). All this is part of what Solomon had in mind when he praised the dead as being better off than the living as the ordinances of the living are often not accepted by their contemporaries.
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Rashbam

והשיכותי, the word is derived from שככה, “calmed down,” as in Esther 7,10 which describes the king’s state of mind once Haman at whom he had been furious had been hanged.
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