Abstract
By applying double and triple angle identities for hyperbolic and trigonometric cosine functions, we obtain closed-form evaluations for two families of infinite products involving nested radicals.
Highlights
Û × Ö Ø ÓÒ Ð ÑÙÐØ ÔÐ × Ñ Ô Ô Ö Ë ÖÚ Ð×Ó. Ö × Ñ Ð Ò ØÓ Ø Î Ø Ò¬Ò Ø ÔÖÓ Ù Ø ÓÚ o.
É Þ Þ 1⁄2 Ù× Ø × ÐÓ× 1 ÓÖÑ ÜÔÖ ×× ÓÒ ØÓ ØÖÛØØ
ÖÓÑ Ë ÖÚ 3× ÛÓÖ Û ÒØ Ò Ò Ø × Ô Ô Ö ØÓ ×Ø Ð × ÐÓ× 1 ÓÖÑ
Summary
Û × Ö Ø ÓÒ Ð ÑÙÐØ ÔÐ × Ñ Ô Ô Ö Ë ÖÚ Ð×Ó. Ö × Ñ Ð Ò ØÓ Ø Î Ø Ò¬Ò Ø ÔÖÓ Ù Ø ÓÚ o. É Þ Þ 1⁄2 Ù× Ø × ÐÓ× 1 ÓÖÑ ÜÔÖ ×× ÓÒ ØÓ ØÖÛØØ ÖÓÑ Ë ÖÚ 3× ÛÓÖ Û ÒØ Ò Ò Ø × Ô Ô Ö ØÓ ×Ø Ð × ÐÓ× 1 ÓÖÑ
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