Appendix 1. Some Useful Formulae

Appendix 1. Some Useful Formulae - Appendix: Some Useful...

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0-8493-????-?/00/$0.00+$.50 © 2000 by CRC Press LLC © 2001 by CRC Press LLC Appendix: Some Useful Formulae Sum of Integers and Their Powers k nn k n k k n n n kn k k n k n k n k n k n k n = + = ++ = + = + −= = = = = = = () ( ) ( ) ( ) ( 1 2 12 1 6 1 2 22 13 3 1 30 21 4 1 2 1 3 1 3 4 1 2 1 2 2 1 2 += + = = 1 3 2 1 1 3 5 12 3 1 22 2 1 ) ()( ) ( ) n kk n n k n k n
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© 2001 by CRC Press LLC Arithmetic Series Geometric Series Arithmo-Geometric Series Taylor’s Series () [ ( ) ] ak r n an r k n += + = 0 1 2 21 aq aq q q k k n n = = 1 1 1 1 1 [( ) ] r q aan r q q rq q q q k n k nn −+− + = 0 1 1 2 1 1 1 1 1 fx a f x a k fx ay b fxy a f x b f y a f x b f y ab f xy k k k ( ) ! (,) ( , ) ! ++ = + + + + + +… = 0 2 2 2 2 2 2 2 1 2 2 ∂∂
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© 2001 by CRC Press LLC Trigonometric Functional Relations Relation of Trigonometric and Hyperbolic Functions sin( ) sin( ) sin ( ) cos ( ) cos( ) cos( ) cos ( ) cos ( ) cos( ) cos( ) sin ( ) sin ( ) sin x y xy x y x y x y y x x ±= ± += + −= + 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 1 2 m =± + = =− 1 2 1 1 2 1 2 1 22 33 4 44 8 1 34 3 4 3 3 2 3 ( cos( )) cos ( cos( )) sin(
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Appendix 1. Some Useful Formulae - Appendix: Some Useful...

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