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FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: Index of Notations (a), =r(a+n)/r(a) (Pochhammer’s symbol)---- al(q) characteristic value of Mathieu’s equation- - A(z) =2P(z) - 1 normal probability function- _ _ _ Ai(z) Airy function _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ A.G.M. arithmetic-geometric mean..-- - _ _ - _ _ _ - - - am z amplitude of the complex number z _ _ _ _ _ _ _ _ antilog antilogarithm (log-’) _ _ - - - - - - - - - - - - - - - - - arcsin z, arccos z inverse circular functions- - - - - - arctan z, arccot z arcsec z, arccsc z arctanh z, arccoth z arcsech z, arccsch z arcsinh z, arccosh z inverse hyperbolic functions-- arg z argument of z _ ~ _ _ ~ ~ ~ ~ ~ _ _ _ ~ ~ ~ ~ _ ~ ~ ~ ~ ~ ~ ~ a,(*) characteristic value of Mathieu’s equation- - B , Bernoulli number _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ B,,(z) Bernoulli polynomial- - - - - - - - - - - - - - - - - - - - berg, beig, Kelvin functions- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Bi(z) Airy function _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ cd, sd, nd Jacobian elliptic functions _ _ _ _ _ - - - - - - - c.d.f. cumulative distribution function - - - - - - - _ _ - ce,(z, q) Mathieu function . . . . . . . . . . . . . . . . . . . . . on Jacobian elliptic function.. - - - - - - - - - - - - - - - - - - e n , Dn, Sn integrals of the squares of Jacobian elliptic functions.. - - - - - - - - - - - - - - - - - - - - - - - - - cs, &. ns Jacobian elliptic functions _ _ _ _ _ _ _ _ _ _ _ _ C(z) Resnel integral _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ C,(z) Chebyshev polynomial of the second kind-- C(z, a) generalized Fresnel integral- - - _ _ - - - _ _ - - - Cer(z, q) modified Mathieu function- _ _ _ _ _ _ _ _ _ _ _ Cl(z), Cz(z) Fresnel integrals _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ C,,(a) (2) ultraspherical (Gegenbauer) polynomial- - Chi(z) hyperbolic cosine integral- - - - - - - - - - - - - - - Ci(z) cosine integral-_ - - _ _ _ - - - - _ _ - - - - _ _ - - _ _ - _ _ Cin(z) cosine integral-- - - _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ - - Cinh(z) hyperbolic cosine integral- - - - - - - - - - - - - - colog cologarithm _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ covers A, coversine A _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ^ _ _ dc, x, sc Jacobian elliptic functions- - ___ _ _ - _ _ - - dn=A( q) delta amplitude (Jacobian elliptic func- tion)_------------------------------------ D,(z) parabolic cylinder function (Whittaker’s f o r m ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - - - - - - - - - - - - - - - - el, ez, e3 roots of a polynomial (Weierstrass form)-- e* exponential function _ _ _ _ - - - - - - - - - _ _ - - _ _ - _ _ - - e,(z) truncated exponential-function- _ - - - - - - - - - - E(p\a) elliptic integral of the second kind- - - - - - E(a,z) parabolic cylinder function- _ _ - - _ _ - - - - _ _ - E.(z) Weber’s function _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ E,(m)(z) Weber parabolic cylinder function--_---- E(m) complete elliptic integral of the second kind__----------------------------------- 1044 Page 256 722 931 446 571 16 89 79 86 16 722 804 804 379 446 570 927 725 569 576 570 300 774 262 732 300 774 231 23 1 231 231 89 78 570 569 687 629 69 262 589 693 498 509 590 Ei(z) exponential integral- _ - - _ - - - _ - - - - - - - - - - - - El@) exponential integral- - _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ - E [ g ( X ) ] expected value operator for the function Ein(z) modified exponential integral.. - - - - - - - - - - - En Euler number _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ E,[z) Euler polynomial- - _ _ - - - _ _ _ _ _ _ - _ _ _ _ _ _ - _ _ E,(z) exponential integral--- - - - _ _ - _ _ _ _ - - - - - - _ _ erf z error function _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ erfc z complementary error function- _ _ - - - - _ _ _ _ - exp z=e* exponential function- - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ exsec A, exsecant A _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ fc,,, fo,, joining factors for Mathieu functions---- F(a, b; c; z) hypergeometric function _ _ _ _ _ _ _ _ _ _ _ F( p\a) elliptic integral of the first kind - - - - __ - - - F ~ ( v , p ) Coulomb wave function (regular) ___ - _ _ _ _ FPP fundamental period parallelogram- - - - - _ - - - ,F,(uI, . . ., a,; bl, . . ., b,; z) generalized hyper- - - - - - - _ - - - - - - _ - - - - _ - - - g2, g3 invariants of Weierstrass elliptic functions- - ge,r, qo.. joining factors for Mathieu functions--- g(z, y, p) bivariate normal probability function..-- Gi(z) related Airy function _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ G& p ) Coulomb wave function (irregular or loga- rithmic)_--__-_--------------------------- C,(p, 9,s) Jacobi polynomial _ _ _ - _ _ _ _ _ _ - - _ _ _ - _ - gd(z) Gudermannian _____ _ - - _ - - - - - _ - - - - - - - _ - - - h!,“(z) spherical -Bessel function of the third kind- hav A haversine A _ _ _ _ __ _ __ _ _ _ _ _ __ _ _ _ __ _ _ _ _ _ _ H,(z) Struve’s function- - - _ - ___________- __- - _- Hi(z) related Airy function - He,(z) Hermite polynomial ____ - - - - - - - _ _ _ - - - _ _ _ HP)(z) Bessel function of the third kind (Hankel) - g(z) -_-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - _ - _ - - - geometric function . . Page 228 228 928 228 804 804 228 297 297 69 78 735 556 589 538 629 556 629 740 936 448 538 774 77 437 78 496 448 775 358 Hh,(z) Hh (probability) function _ _ _ _ _ _ _ _ _ _ _ _ _ 300,691 H,(z) Hermite polynomial- - - _ - _ _ - _ _ _ - - - _ _ _ _ _ - H(m, n, z) confluent hypergeometric function--..- Z.(z) modified Bessel function ____ _ - - - _ _ _ _ _ _ _ _ _ - m Z , , + % ( z ) modified spherical Bessel function of the first kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -Z-,,-%(z) modified spherical Bessel function of the second kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Z(u, p ) incomplete gamma function (Pearson’s form)-_----__---_-_----------------_----- Z+(a, b) incomplete beta function __- - - _- __- - - - - - j z imaginary part of z(=y) . . . . . . . . . . . . . . . . . . . . i n erfc z repeated inte\$al of the error function--.. j,(z) spherical Bessel function of the first kind-_- J,(z) Anger’s function- - - - - - - - _- - _ _ __- - - _ _ - - _- J , ( z ) Bessel function of the first kind _ _ _ _ _ _ _ _ _ _ _ k modulus of Jacobian elliptic functions-_- - - - - - - k‘ complementary modulus-- - - - - - - - - - - - - - - - - - - k , ( z ) Bateman’s function _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - 775 695 374 443 443 262 263 16 299 437 498 358 590 590 510 The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States.