[Machine] I have never seen the Messenger of Allah ﷺ waving his hands while making supplication on the pulpit or anywhere else. But I have seen him saying this and pointing with his index finger while holding his middle finger with his thumb. The purpose of both narrations is to affirm the supplication in the sermon. It is also from the Sunnah that he does not raise his hands while making supplication in the sermon, but he only gestures with his finger. It is confirmed from Anas ibn Malik that the Prophet ﷺ extended his hands and made supplication when he sought rain during the Friday sermon. We also narrated from Anas ibn Malik that the Prophet ﷺ did not raise his hands in any of his supplications except when seeking rain, to the extent that the whiteness of his armpits could be seen. We also narrated from Al-Zuhri that he said: When the Messenger of Allah ﷺ would deliver the Friday sermon, he would make supplication and gesture with his finger, and the people would feel at ease. This was narrated by Qurrah ibn Abdul Rahman from Al-Zuhri from Abu Salamah from Abu Hurayrah, but it is not authentic and Allah knows best.  

مَا رَأَيْتُ رَسُولَ اللهِ ﷺ شَاهِرًا يَدَيْهِ قَطُّ يَدْعُو عَلَى مِنْبَرِهِ وَلَا عَلَى غَيْرِهِ وَلَكِنْ رَأَيْتُهُ يَقُولُ هَكَذَا وَأَشَارَ بِالسَّبَابَةِ وَعَقَدَ الْوُسْطَى بِالْإِبْهَامِ وَالْقَصْدُ مِنَ الْحَدِيثَيْنِ إِثْبَاتُ الدُّعَاءِ فِي الْخُطْبَةِ ثُمَّ فِيهِ مِنَ السُّنَّةِ أَنْ لَا يَرْفَعَ يَدَيْهِ فِي حَالِ الدُّعَاءِ فِي الْخُطْبَةِ وَيَقْتَصِرَ عَلَى أَنْ يُشِيرَ بِأُصْبُعِهِ وَثَابِتٌ عَنْ أَنَسِ بْنِ مَالِكٍ عَنِ النَّبِيِّ ﷺ أَنَّهُ مَدَّ يَدَيْهِ وَدَعَا وَذَلِكَ حِينَ اسْتَسْقَى فِي خُطْبَةِ الْجُمُعَةِ فَرُوِّينَا عَنْ أَنَسِ بْنِ مَالِكٍ عَنِ النَّبِيِّ ﷺ أَنَّهُ كَانَ لَا يَرْفَعُ يَدَيْهِ فِي شَيْءٍ مِنْ دُعَائِهِ إِلَّا فِي الِاسْتِسْقَاءِ حَتَّى يُرَى بَيَاضُ إِبْطَيْهِ وَرُوِّينَا عَنِ الزُّهْرِيِّ أَنَّهُ قَالَ كَانَ رَسُولُ اللهِ ﷺ إِذَا خَطَبَ يَوْمَ الْجُمُعَةِ دَعَا فَأَشَارَ بِأُصْبُعِهِ وَأَمَّنَ النَّاسُ وَرَواهُ قُرَّةُ بْنُ عَبْدِ الرَّحْمَنِ عَنِ الزُّهْرِيِّ عَنْ أَبِي سَلَمَةَ عَنْ أَبِي هُرَيْرَةَ مَوْصُولًا وَلَيْسَ بِصَحِيحٍ وَاللهُ أَعْلَمُ