By Dr. Wilhelm Magnus, Dr. Fritz Oberhettinger, Dr. Raj Pal Soni (auth.)
Read Online or Download Formulas and Theorems for the Special Functions of Mathematical Physics PDF
Similar physics books
Balancing concise mathematical research with the real-world examples and functional functions that encourage scholars, this textbook offers a transparent and approachable creation to the physics of waves. the writer indicates via a extensive technique how wave phenomena could be saw in a number of actual events and explains how their features are associated with particular actual principles, from Maxwell's equations to Newton's legislation of movement.
In recent years a brand new discussion has started among the average sciences and the arts. this can be really real of physics and philosophy, whose sphere of mutual curiosity multiplied considerably with the appearance of quantum mechanics. between different issues, the dialogue covers the evolution of theories, the function of arithmetic within the actual sciences, the conception and cognition of nature and definitions of area and time.
Molecular Physics and Hypersonic Flows bridges the space among the fluid dynamics and molecular physics groups, emphasizing the function performed through effortless techniques in hypersonic flows. specifically, the paintings is essentially devoted to filling the space among microscopic and macroscopic remedies of the resource phrases to be inserted within the fluid dynamics codes.
- Mathematical Methods in the Physical Sciences 3rd [Instuctor's Solutions Manual]
- Mathematical Methods for Physicists: A Concise Introduction
- SN 388ACCEP
Additional info for Formulas and Theorems for the Special Functions of Mathematical Physics
11·12 + + ... J ' C(7) 7·11 ·12 ·13 ·14 +... J. 36 I. The gamma function Power series expansions of some trigonometric and hyperbolic functions -f= sm z zcotz= . 2 i ,,=0 (-It (1 - 22n - 1) B2"1 z2n, (2n) . B L (-It 22n~z2" ,,=0 (2n). 00 = - 2~ C~2~) z2n, Izl < n, tan z = ~ (_1),,+1 22n (22n _ 1) B2"1 ,,~ = 2 i' (22:~ (2n). z2n n(2n)! JzJ < ' 1/;2' tanh z = 2 coth (2z) - coth z 1: 2 (22n - 1) B 2n z2n-1 2 1: (_1)n+1 (22"1/;~ C(2n) z2n-1, = 2" (2n)1 n=1 = 1) ,,=1 z coth z = z [2 Jzl < ~ , + e'2z-1 sinh ( z -2--- ~)] 1 + log (1 _ log - - - - = -z 2 e-Z) ~~ z 00 _ "" B 2" z2n , z I J < 2n.
1 Linear transformations 2Fl(a, b; c; z) = (1 - zy-a-b ~l(C - a. c - b; c; z), 2F1 (a, b; c; z) = (1 - z) -a ~1 (a. - 1) , 2Fl (a, b; c; z) = (1 - Z)-b ~l (b. 1-)z a. c - b'• c - a - b + 1'1 . - z) , b =1= ± m, m = 0, 1, 2. • . ) _ r(c) r(c - a - b ) . 2F d a• b. c, z - r(c _ b) r(c _ a) ~da. b. a + (1 - z )C-a-b r(c) r(a) r(a + b - c) F ( r(b) 2 1 C- larg (1 - z) I <~, c - a - 48 II. The hypergeometric function 2F( 1 a, 1) ·) ( )-a 2F 1 ( a, a - e +1',a - b+1·'z b· ,e, z = T(c)T(b-a) T(b) T(c _ a) -Z T(c) T(a - b) + 1,.