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 formulas942 PROBABILITY 26.4.22 Pearson Typo I11 v=2ab+2, x2=2b(2+a) 26.4.23 Incomplete moments of Normal distribu- tion x2=P, v=n+l 26.4.24 Generalized Laguerre Polynomials x=xa/2, a=v/2 FUNCTIONS Non-Central XS Distribution Function 26.4.25 where A20 is termed the non-centrality param- eter. Relation of Non-Central xz Distribution With v=2 to the Integral of Circular Normal Distribution (u*=l) Over an Offset Circle Having Radius R and Center a Dis- tance r = f i From the Origin. (See 26.3.21r26.3.27.) 26.4.26 Approximations to the Non-Central x* Distribution Approximating Function 26.4.27 x2 distribution 26.4.28 Normal distribution 26.4.29 Normal distribution Approximation P(X'Z(v, X) = P ( x ) , 2=[m] 2 x f 2 3 -[$-lT Approximations to the Inverse Function of Non-Central x3 Distribution If &(x;~/Y, A)=p, &(x",v*)=p, and &(zp)=p then Approximating Variable 26.4.30 x2 xia = ( 1 + b)x: Approximation to the Inverse Function 26.4.31 Normal 26.4.32 Normal

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