A comparative study of functional equations characterising sine and cosine |
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Authors: | J. C. Parnami H. L. Vasudeva |
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Affiliation: | (1) Dept. of Mathematics, Panjab University, 160014 Chandigarh, India |
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Abstract: | A comparative study of the functional equationsf(x+y)f(x–y)=f2(x)–f2(y),f(y){f(x+y)+f(x–y)}=f(x)f(2y) andf(x+y)+f(x–y)=2f(x){1–2f2(y/2)} which characterise the sine function has been carried out. The zeros of the functionf satisfying any one of the above equations play a vital role in the investigations. The relation of the equationf(x+y)+f(x–y)=2f(x){1–2f2(y/2)} with D'Alembert's equation,f(x+y)+f(x–y)=2f(x)f(y) and the sine-cosine equationg(x–y)=g(x)g(y) +f(x)f(y) has also been investigated. |
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Keywords: | Primary 39C05 |
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