tailieunhanh - Ebook Handbook of mathematical functions with formulas, graphs, and mathematical tables: Part 2

Part 2 book “Handbook of mathematical functions with formulas, graphs, and mathematical tables” has contents: Coulomb wave functions, hypergeometric functions, weierstrass elliptic and related functions, elliptic integrals, mathieu functions, parabolic cylinder functions, combinatorial analysis, . and other contents. | 14. Coulomb Wave Functions Milton Abramowitz 1 Contents Page Mathematical Properties. 538 . Differential Equation Series Expansions. 538 . Recurrence and Wronskian Relations. 539 . Integral Representations. 539 . Bessel Function Expansions. 539 . Asymptotic Expansions. 540 . Special Values and Asymptotic Behavior. 542 Numerical Methods. 543 . Use and Extension of the Tables. 543 References. 544 Table . Coulomb Wave Functions of Order Zero .5 n 20 l P 20 . 546 FoGbp Ơo0z p ỡo0bp 1J .5 .5 2O p l l 20 5S Table . Co ij - T r l iij I. 554 n 0 .05 3 6S The author wishes to acknowledge the assistance of David s. Liepman in checking the formulas and tables. 1 National Bureau of Standards deceased . 537 14. Coulomb Wave Functions Mathematical Properties . Differential Equation Series Expansions Differential Equation dp2 p p2 p 0 L a non-negative integer The Coulomb wave equation has a regular singularity at p 0 with indices Z-M and L it has an irregular singularity at p 00. General Solution w C 17 t pHGƠlGĩ p Cl Cl constants where Fl ti p is the regular Coulomb wave function and GL ii p is the irregular logarithmic Coulomb wave function. Regular Coulomb Wave Function Fl ij p FL v p CZl rỉ ĩe- M L ỉ-irlí 2Z 2 2ip CM ri P n p i Aị rìpk-L- Al 1 1 k E k-L-V AỈ k L 2 F L Fl p CM p t p p 7 p - s Irregular Coulomb Wave Function ơt n p . p c F p ln 2p 1 M p 0L r p Dl ij p l l iị p p C _ _ u p aiW k--L a L l ai i o k L l fc L aỄ 2ijữỉ _1 aỉ-1 2k l pL v AỈ PlM 1 2 i S 1 8 ƠỊI Ị _ _2y 4-- v rir i i Zy pLứ See Table . CM g l i See chapter 6. ớẵ 2 e2 --l - 72 PtC Cpfi 2Í 2Z ịl .in L 2L lj xW_ 1 i 2 4 1 2 . . . Z2 n2 2 2 2L 1 2L 2 r .f y. I - I2fo z 2L l2L P 2L 1 iri-Ddn-L l 2Z-1 2 2 i -Z i - l . . ilj z-l . 2 i 1 ỠL Fah1 2p f p-IFrGbp dp CỈ TỊ Plvu n p 538 COULOMB WAVE .