An Atlas of Functions: with Equator, the Atlas Function Calculator

Front Cover
Springer Science & Business Media, Jul 15, 2010 - Mathematics - 748 pages
0 Reviews

This book comprehensively covers several hundred functions or function families. In chapters that progress by degree of complexity, it starts with simple, integer-valued functions then moves on to polynomials, Bessel, hypergeometric and hundreds more.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

THE HEAVISIDE uxa AND DIRAC FUNCTIONS
75
THE INTEGER POWERS xn AND bx + cn
81
Summing power series Euler transformation Transformations through lozenge diagrams
95
xa
103
Behavior in four quadrants Mellin transforms De Moivres theorem The fractional calculus
113
Ellipticity Geometric properties of the ellipse ellipsoid and semicircle Superellipses
121
THE QUADRATIC FUNCTION ax2 + bx + c AND ITS RECIPROCAL
131
Zeros real and complex The rootquadratic function Conic sections Trajectory of a projectile
139
THE INVERSE CIRCULAR FUNCTIONS
351
PERIODIC FUNCTIONS
367
SINE AND COSINE INTEGRALS 385
384
THE ERROR FUNCTION erfx AND ITS COMPLEMENT erfcx
405
Properties in the complex plane and the Voigt function
427
THE DIGAMMA FUNCTION v
449
THE PARABOLIC CYLINDER FUNCTION Dvx
471
Threedimensional coordinate systems The Laplacian separability and an exemplary application
485

Zeros of cubics and quartics Joining the dots with sliding cubics and cubic splines
147
Finding zeros Rational functions Partial fractions Polynomial optimization and regression
159
Stirling numbers of the first kind Hypergeometric functions
175
Sums of monotonic power series
181
THE LEGENDRE POLYNOMIALSP nx
187
Orthogonality The Legendre differential equation and its other solution the Qnx function
197
Gegenbauer and Jacobi polynomials Fitting data sets with discrete Chebyshev polynomials
209
THE HERMITE POLYNOMIALSHnx
217
THE EXPONENTIAL FUNCTION expx
241
Exponential growthdecay Selfexponential function Exponential polynomial Laplace transforms
256
THE HYPERBOLIC SECANT AND COSECANT FUNCTIONS 281
280
THE INVERSE HYPERBOLIC FUNCTIONS
297
THE SECANT secx AND COSECANT cscx FUNCTIONS
329
THE MODIFIED BESSEL FUNCTIONS Inx OF INTEGER ORDER
507
THE MACDONALD FUNCTION Kvx
527
THE BESSEL FUNCTION Jvx OF ARBITRARY ORDER
553
Behavior close to zero argument Hankel functions Asymptotic expansions of cylinder functions
577
THE AIRY FUNCTIONS Aix AND Bix
585
Kinship with Neumann functions The modified Struve function
603
The associated Legendre functions Solving the Laplace equation in spherical coordinates
627
THE INCOMPLETEELLIPTIC INTEGRALS FkQ AND EkQ
653
THE JACOBIAN ELLIPTIC FUNCTIONS 671
672
THE HURWITZ FUNCTION vu
685
BIBLIOGRAPHY
703
SYMBOL INDEX
723
Copyright

Other editions - View all

Common terms and phrases

About the author (2010)

Keith B. Oldham is a professor of Chemistry at Trent University in Ontario, Canada. He has co-authored several books, contributed to numerous others, and has published over 200 articles. He co-authored, with Jerome Spanier, the first edition of An Atlas of Functions.

Jan C. Myland is a Research Associate in Electrochemistry at Trent University.

Jerome Spanier is a prominent mathematics professor emeritus, currently a researcher at University of California, Irvine. He has received many prestigious honors and awards and has authored or co-authored numerous publications.

Bibliographic information