Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55)
Purchase the electronic edition of this book in Adobe PDF format!
FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | MEDIUM | LARGE

Below is the OCR-scanned text from this page:
1034 INDEX Distribution functions-Continued Page discrete_---_-___________-__________________ 927 inequalities for ______________________________ 931 lattice ______________________________________ 927 one-dimensional continuous- _ - _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ 930 one-dimensional discrete--- - _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ 929 Divisor-functions--_ _ - _ _ _ __ _ _ - _ ___ _ _ _ _ _ ___ - _ ___ 827 tableof __________________________L_________ 840 Double precision operations _____ _ - _ __ _ ___ __ _ __ _ _ 21 E Economization of series _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 791 Edgeworth asymptotic expansion-__ _ __ _ ___ _ _ _ _ 935,955 Einstein functions _____________________________ 999 Elliptic functions Jacobian__--_________-_________-__-_________ 567 Weierstrass_- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - 627 Elliptic integrals- - _ - _ _ _ _ _ . . . . . . . . . . . . . . . . . . . . . 587 amplitude--___-___________-_________--__-__ 590 canonical forms _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 589 characteristic _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - 590 definition-_-________-_-_________-_-__-_____-_ 589 graphs of the complete _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 592 graphs of the first kind . . . . . . . . . . . . . . . . . . . . . 592,593 graphs of the incomplete-.. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 593,594 graphs of the second kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 592, 594 graphs of the third kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 600 modular angle-_-__-__--________-___________ 590 m o d u l u s ~ _ ~ ~ ~ _ ~ _ _ ~ ~ _ _ _ ~ ~ ~ ~ _ ~ ~ ~ ~ _ _ _ _ ~ ~ ~ _ ~ _ _ _ _ 590 of the first kind- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 589 of the second kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 589 of the third kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 590,599 parameter_-_-_-__-__----__-______-_______ 590,602 reduction formulas _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 589,597 reduction to canonical form ____r______________ 600 relation to Weierstrass elliptic functions-_ - _ __ _ - 649 tables of complete _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 608 tables of the incomplete _ _ _ _ _ _ _ _ _ _ 2 _ _ _ _ _ _ _ _ _ _ _ 613 tables of the third kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 625 Elliptic integrals, complete- _ _ - _ - __ _ __ _ - _ __ _ _ _ - _ 590 computation of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ 601 infinite series for-. - _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 591 Legendre’s relation- - _ - - - _ _ _ - _ __ _ _ _ _ ___ __ _ _ __ 591 limiting values _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ 591 of the first kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 590 of the second kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 590 of the third kind _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 599,605 polynomial approximations - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 591 q-series f o r _ - - - _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 591 relation to hypergeometric functions _ _ _ _ _ _ _ _ _ _ _ 591 Elliptic integrals, incomplete--_ __ __ _ __ _ ___ __ _ _ _ - 592 amplitude of any magnitude _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 592 amplitude near 7r/2- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ 593 complex amplitude- - - _ - _ _ __ __ _ - _ ___ __ _ __ _ _ _ _ 592 computations involving _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 595,602,605 imaginary amplitude-__ _ _ _ - _ - - _ __ - _ - - _ - _ _ _ _ __ 594 Jacobi’s imaginary transformation- _ - _ _ - _ _ _ - _ - _ 592 negative amplitude- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 592 negative parameter- - - _ _ - _ _ - - _ - _ - __ _ - _ __ _ _ - _ _ 593 numerical evaluation of - - - _ _ - _ __ _ _ - _ _ _ _ - - _ - - _ 595 (see Jacobian elliptic functions) (see Weierstrass elliptic functions) Page parameter greater than unity _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 593 special cases of__--_-_--__-____-_-__-_____L-_- 594 Elliptical coordinates _ - _ - _ _ _ _ - _ - - _ _ - - _ - - - _ _ - _ _ - 752 Equianharmonic case- _ - _ _ - _ _ - _ _ _ _ _ _ _ _ - _ - _ ___ - _ 652 Error absolute___-____--_-_______-_-_-___-_-_-____ 14 percentage___________-_-__-_--___-__---__-__ 14 relative-_-__-_---___-_-_____-____-_-_______ 14 Error function _ _ _ _ _ _ _ _ _ _ _ _ _ _ 262,297,301,304,306,509 altitude chart in the complex plane _ _ _ _ _ _ _ _ _ _ _ _ 298 asymptotic expansion of_-_ - _ - - _ _ - __ _ __ - _ _ _ - _ _ 298 complex zeros o f _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ - _ _ _ - _ - 329 continued fraction for _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 298 definite and indefinite integrals related to____ ___ 302 derivatives of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ _ _ _ 298 graphs of_______-_____--__-_-__-_-_____-__-- 297 inequalities for ______________________________ 298 infinite series approximation for the complex function__-___-__-____-__-_____-___-_-_-_- 299 integral representation of_- - _ _ _ - _ _ _ _ _ - - __ _ - - - _ 297 rational approximations - _ _ _ _ _ _ - _ - _ _ _ - _ _ - _ _ - _ - 299 relation to the confluent hypergeometric function- 298 repeated integrals of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 299 series expansions for _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 297 symmetry relations- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 297 table for complex arguments _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 325 table of repeated integrals of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 317 tables of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - _ _ _ - _ 310,312,316 value at infinity _____________________________ 298 Eta functions_________-__--_--_-__-__-__-_-_-- 577 Euler function ________________________________ 826 table o f _ _ _ _ _ _ , _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ _ - _ - _ - _ _ _ _ - - 840 Euler-Maclaurin formulas- - - _ _ _ _ - _ _ _ - _ - _ _ - - __ - _ 806 Euler-Maclaurin summation formula--- _ _ 16, 22, 806, 886 Euler numbers ________________________________ table o f __ __ _ _ _ _ _- _ __ _ _ __ _ _ _ _ _ _- _ _ _ _- - _ _ _ _ _- Euler polynomials- _ _ _ _ _ _ _ . . . . . . . . . . . . . . . . . . . . . as sums of powers _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ coefficients of - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ derivatives o f _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ differences o f _ _ _ _ _ _ _ - _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ - _ _ expansions of______-_____-_____-___-___-____ Fourier expansions of_ _ _ - _ _ _ - _ __ _ _ _ _ _ - - _ _ _ _ - - generating function for__ - _ _ _ _ _ __ _ _ _ _ _ _ _ _ - _ __ _ inequalities for _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ - - _ _ integrals involving-- _ _ - _ - _ _ _ _ _ - _ - _ _ _ - - _ _ _ _ - - _ multiplication theorem for- _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ relations with Bernoulli polynomials - _ _ _ _ ____ _ - - special values of _________________________- - - - symbolic operations ____ _ _ _ _ _ _ _ __ - _ _ _ - _ _ _ _ _ _ - - symmetry relations - - _ _ _ _ - - _ _ _ _ _ _ - _ _ - - _ - _ _ - - _ Euler summation formula- _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Euler-Totient function _ _ _ _ _ _ - _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ - - Euler’s constant____--___-__-___-_--____-____-- 804 810 803 804 809 804 804 804 805 804 805 805 804 806 805 806 804 806 826 255 Euler’s formula _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 74,255 Euler’s integral ________________________________ 255 Euler’s transformation of series- - - - - _ _ _ _ _ _ _ _ _ _ _ _ 16,21 Everett interpolation coefficients _ _ _ - - _ - - _ _ _ _ - _ - _ 880 relation to Lagrange coefficients- - _ _ _ - - _ - _ _ _ _ - - 880 Everett’s formula _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 880,883 Excess---_--__-__-_--------_--_____-_-_____-- 928