By Ferrers, N. M. (Norman Macleod)

This quantity is made from electronic photographs from the Cornell collage Library ancient arithmetic Monographs assortment.

**Read or Download An elementary treatise on spherical harmonics and subjects connected with them PDF**

**Best calculus books**

**Advances on Fractional Inequalities**

Advances on Fractional Inequalities use essentially the Caputo fractional spinoff, because the most vital in purposes, and offers the 1st fractional differentiation inequalities of Opial kind which consists of the balanced fractional derivatives. The e-book maintains with correct and combined fractional differentiation Ostrowski inequalities within the univariate and multivariate situations.

This quantity comprises complaints from the AMS convention on utilized research held at LSU (Baton Rouge) in April 1996. issues comprise partial differential equations, spectral thought, practical research and operator concept, complicated research, numerical research and comparable arithmetic. purposes contain quantum idea, fluid dynamics, regulate idea and summary matters, reminiscent of well-posedness, asymptotics, and extra.

This ebook offers an creation to the idea of distinction equations and recursive family members and their purposes.

- Analytic Sets in Locally Convex Spaces
- Funktionentheorie 1
- Calculus: Solution Manual (5th Edition)
- The history of the calculus and its conceptual development
- Analysis
- Multivariable Calculus, Ninth Edition

**Extra info for An elementary treatise on spherical harmonics and subjects connected with them**

**Sample text**

4 being any even integer. "(i + 2) 1 . 3 ... 4... (i-2)" ZONAL HARMONICS. 22. , must be expressible in terms To determine this expression, assume function of /uT PJ_ I} Pi-3 "' , of dP. -. '. 1, > m, ^^= or i when p = = 1 From the limits be, equal to - 5) P . + (2i - (2i 4 2 cZju, 23. pj 3 (2t- 1) 9) P^ P^. rift this equation we deduce and 1 being taken, in order that at the superior limit. P f P ( _2 may ZONAL HAKMONICS. 38 to the fundamental equation for a zonal see that Now, recurring harmonic, we 1 24.

L)'P /*'+. 4 22 . ZONAL HAKMONICS. ^, Hence when assume, /A is written for /A. respectively = or according as i is even or odd. That is, P. involves only odd, or only even, powers of i, according as i is odd or even*. P/... P P ' 4 , l l , Assume then Our to determine is A A^.... 4 2 Then, multiplying successively by ^~ /uT ... and inte1 to + 1, we obtain the following system of grating from object t , , equations : _^ + _^_ + 13 i_3 j nr /^ 2*? And , I o 2? er L 1*=! _ + i i o 2t-5 ' ...

U f? . 9;6 P 2< I _1_ ~ / "'I (f)'\ v-' y* For each of these expressions, when substituted for V, 2 the equation V V = 0, and they become respectively is put = 0, and equal to (1) and (2) when consequently satisfies r = z. ') becomes equal to (2') when r = c, and will great, therefore denote the required potential for all values of r less than c. These expressions means may be reduced to other forms by of the expressions investigated in Chap. 2, Art. 25, viz. Or P. 3 APPLICATION OF ZONAL HARMONICS 46 which is equivalent to M The brings it substitution of the last form of into the form 1 fa c*_ 2t{2 + (2?