Appendix 1. Some Useful Formulae

# Appendix 1. Some Useful Formulae - Appendix Some Useful...

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
© 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 ∂∂
© 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(

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online