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Fourier_series_integral_identities.gif (500 × 275 pixels, file size: 188 KB, MIME type: image/gif, looped, 43 frames, 1 min 8 s)

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العربية: تعامد دوال الجيب وجيب التمام يجعل تكامل مضروب زوج منهم صفرا.
Ελληνικά: Τα ημίτονα και τα συνημίτονα σχηματίζουν ένα ορθοκανονικό σύνολο, όπως απεικονίζεται παραπάνω. Το ολοκλήρωμα του ημιτόνου, του συνημιτόνου και το γινόμενό τους είναι ίσο με μηδέν (οι πράσινες και οι κόκκινες περιοχές είναι ίσες και έχουν ακυρωθεί) όπου m, n ή οι συναρτήσεις είναι διαφορετικές, και π μόνο όταν τα m και n είναι ίσα, και η συνάρτηση που χρησιμοποιείται είναι η ίδια.
English: Sines and cosines form an orthonormal set — that is, the integral of sine, cosine and their product is equal to zero (green and red areas are equal, and cancel out) when m, n or the functions are different, and equal to pi only if m and n are equal, and the function used is the same.
中文：正弦和餘弦形成了正交集合。正弦、餘弦及其乘積的積分，當m與n不同或二函數不同時是0(綠色和紅色區域相等抵消)，僅當m和n相等並且函數相同時為π。.
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Author Lucas Vieira
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29 March 2011

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current19:05, 29 March 2011Thumbnail for version as of 19:05, 29 March 2011500 × 275 (188 KB)LucasVB{{Information |Description ={{en|1=The five integral identities that make Fourier series work.}} |Source ={{own}} |Author =Kieff |Date =2011-03-29 |Permission = |other_versions = }} [[Category:Mathematical

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