Download Phraseology: Thousands of Bizarre Origins, Unexpected by Barbara Kipfer PDF

By Barbara Kipfer

The awesome secrets and techniques of the words We Use Everyday

Phraseology is the final word number of every little thing you by no means knew concerning the fabulous words present in the English language. It includes information regarding word historical past and etymology; strange, misplaced, or unusual words; how words are shaped; and greater than 7,000 proof approximately universal English phrases.

Practical sufficient for use as a reference booklet yet so enjoyable that each publication lover probably want to learn it directly via, phrasing comprises such engrossing tidbits as:

• around the BOARD is an allusion to the board showing the chances in a horse race
• ARTESIAN good will get its identify from Artois, the place such wells have been first made
• top guy originated in Scotland, the place the groom abducted his bride simply by buddies, together with the hardest and bravest - the simplest guy.

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Extra info for Phraseology: Thousands of Bizarre Origins, Unexpected Connections, and Fascinating Facts about English's Best Expressions

Sample text

Il} ~/ 2 (l-p. 2 )/ 4} · Y(z) =0 (3b) Section 3. Related Differential Equations 33 with the solution (3a) We now consider a number of particular applications of these formulae. I. = 0 and A= 1 in Eq. (3a), then we see directly that the function y(z) = P,,I'12 (Az) satisfies the differential equation 1-p2} "A A2 y"(z)+ { --+-+~4z2 ·y(z)=O. 2'la, t ·o/1 + 4c (2 V~· z) · Y (z) (4{J) If A= 1 in equation (4a) then the resulting differential equation is 1 4 y"(z)+ { - - 1X -J12 ++- 4z z 2 } · y(z)=O.

The formulae showing the connection between these various particular solutions of The Various Forms of the Differential Equation 40 Eq. (22) could be derived directly from the differential equation. Our approach, however, is to derive these relationships from those already shown for the various solutions of Whittaker's differential equation. ,,. 7 to be always linearly independent, correspond to the functions D,(z) and D_,_ 1 (± iz) in the case now under consideration. In fact, we have the exact correspondence as given in Eq.

1- s2) -2-. G+ :r ds -1 J 1+1' ,. = 2-l'z~ e•i2·cosrp. sin~' 0 · 0 The two Hankel integrals, Eqs. )r(1+p-A) z 1 jx'--1 ·(1-x)ll-'-· 1F 1 0 (14) 1+1' . -2-. ) > -1 Section 2. 12 (z}. In particular the following relation follows from Eq. Jt. 1 (z) x,p2 = 1/1 n (1+p ) r - 2- - x r(2x) . 2"-p/2 . zl12+x . e-z/2 (14a) 1 -jxPf2-x . (1- x)2x-l. /2-x(~28). e"z/2 . dx. Re(x) > 0, Re(,u- 2x) > -1. 1. and x which severely restrict the validity of Eq.

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