MATHEMATICAL REFERENCE / AMS55

Handbook of Mathematical Functions

Abramowitz and Stegun's classic collection of formulas, graphs, and mathematical tables. Original page scans and deep links are preserved.

ChapterChoose a chapterTitle PagePrefaceForewordContentsIntroduction1. Mathematical Constants2. Physical Constants and Conversion Factors3. Elementary Analytical Methods4. Elementary Transcendental Functions Logarithmic, Exponential, Circular and Hyperbolic Functions5. Exponential Integral and Related Functions6. Gamma Function and Related Functions7. Error Function and Fresnel Integrals8. Legendre Functions9. Bessel Functions of Integer Order10. Bessel Functions of Fractional Order11. Integrals of Bessel Functions12. Struve Functions and Related Functions13. Confluent Hypergeometric Functions14. Coulomb Wave Functions15. Hypergeometric Functions16. Jacobian Elliptic Functions and ThetaFunctions17. Elliptic Integrals18. Weierstrass Elliptic and Related Functions19. Parabolic Cylinder Functions20. Mathieu Functions21. Spheroidal Wave Functions22. Orthogonal Polynomials23. Bernoulli and Euler Polynomials, Riemann Zeta Function24. Combinatorial Analysis25. Numerical Interpolation, Differentiation and Integration26. Probability Functions27. Miscellaneous Functions28. Scales of Notation29. Laplace TransformsSubject IndexIndex of Notations

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Scanned text; use the page image to verify formulasWEIERSTRASS ELLIPTIC AND RELATED FUNCTIONS 639 Other Series Involving @ Series near zo [ @(zO)=O1 18.5.52 +7( 12~i-5~:) 13 84~:-10~: u8- 1363~&u'O 3 33 5e2( 55~:-2316~i)u'~ + 5c3L4 + 33czc3ue+ I+. . . 143 + 18.5.53 where u=( z-zo), @: = @ '( zo)=i& 18.5.54 u= @:[o+at~+2a2~3+ + 1 5g3 @ A2 +70a3)v6 + 2a2( 2 @A4+7g3 @ i2+ 2ia3)v6 +( g++ I g;+20a3 1 @;4+ 1ija2g3 p;q + 16016 a6g3@ h2+ 19448 a') do]+ . . . where v= @ /(@ ;)2 and a=g2/4 18.5.55 Series near wf 18.5.56 (@ - e f ) = (3e:-5ca)u+ (10c2ei+21c3)u2+ (7c2et +21c3ef+5c:)u3+ (18c3e:+30ciei 92c2c3e,+ 1054 45750 c24 +g 4) u7+ . . ., 3405 + -ij- 4cae t + 143 18.5.57 where u= (z- wJ2 Other Series Involving @ I Series near z, 18.5.58 (@ '- @ A)=[ - 10czu-56c3u3+30c~u5+264c2c3u7 (840&-100~,3) 54526% 11 uQ--..-..- U + 3 11 7OC2(55~,"-2316e",) 143 + 18.5.59 where u = (2- zo) 18.5.60 3@; ( z-zO)=A- bA3- - A4 + 3( CZ + b2)A5 2 +lob@ ;A6-3[36c3-3@ ;+4b3]A7 -3@ 6 (z c2+21b2 ) A"+% (285b2c2 +1004-279@ 18.5.61 where A= (@ '- @ A)/(- 10~2) 18.5.62 and b = 4g3/g2 Series near wf 18.5.63 @ ' = 2 (34 - 5c2) a! + 4 ( 10c2ef + 2 1c3) a3 + 6 (7c2e: + 2 1 c3er+ 54) a!'+ 24 (6c3e: + 1 Ocie , 92c2c3e , + 1056 +..., 18.5.64 where a=(z-of).

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