Wang Z.X., Guo D.R., Xia X.J. — Special Functions :: Электронная библиотека попечительского совета мехмата МГУ

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Wang Z.X., Guo D.R., Xia X.J. — Special Functions

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Название: Special Functions

Авторы: Wang Z.X., Guo D.R., Xia X.J.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 720

Добавлена в каталог: 05.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Addition formula      362 395 573
Addition formula, ${C}_{n}^{\lambda}(x)$       290
Addition formula, E(u)      557
Addition formula, Z(u)      569
Adjoint      79
Adjoint, equation      79
Adjoint, operator      79
Airy integral (function)      436
Appell function      208
Appell's hypergeometric functions of two variables      192
Approximate solutions      640
Associate Legendre, equation      71 89 211
Associate Legendre, functions      211 233
Associate Legendre, functions, first kind      441
Associate Legendre, functions, first kind, order fi and degree v      248
Associate Legendre, functions, first kind, order m and degree I      234
Associate Legendre, general ${P}_{\nu}^{\mu}(z)$       247
Associate Legendre, general ${P}_{\nu}^{\mu}(z),$ second kind      442
Associate Legendre, general ${P}_{\nu}^{\mu}(z),$ second kind, order $\mu$ and degree $\nu$       251
Associate Legendre, general ${P}_{\nu}^{\mu}(z),$ second kind, order m and degree l      234
Asymptotic expansion, Bessel functions for large $|\nu|$ and       384
Asymptotic expansion, fundamental properties      31
Asymptotic expansion, general      29
Asymptotic expansion, general, Modified Bessel function of the second kind      380
B(Beta)-function      103
Barnes integral representation      304
Barnes integral representation, double      208
Barnes, contour      156
Barnes, lemma      163
Bateman expansion formula      440
Bernoulli numbers      2
Bernoulli polynomials      1
Bernoulli polynomials, Fourier expansions      42
Bernoulli polynomials, integral representation      41
Bernoulli polynomials, multiplication formula      41
Bernoulli polynomials, order n and degree $\nu$       42
Bessel, equation      67 89 345
Bessel, equation, order half an odd integer      346
Bessel, equation, with imaginary argument      374
Bessel, functions      345
Bessel, functions, first kind of order $\nu$       348
Bessel, functions, integral order      359
Bessel, functions, second kind ${Y}_{\nu}(z)$       365 366
Bessel, functions, third kind      366
Bessel, functions, zero      420
Bessel, inequality      38
Bessel, representation      364
Bi-spherical coordinates      671
Bilinear concomitant      79
Binet, first formula      110
Binet, second formula      110 122
Cardan's formula      655
Cauchy formula      132
Characteristic exponents      615 648
Chebyshev function second kind      206
Chebyshev polynomial      173
Chebyshev polynomial, generating function      176
Chebyshev polynomial, second kind      206
Closure property      38
Complementary modulus      511
Complete elliptic integrals      511 535
Complete elliptic integrals, first kind      460
Complete elliptic integrals, second kind      552
Complete elliptic integrals, third kind      553
Completeness ${P}_{l}^{m}(x)$       239
Completeness relation      38
Components $({u}_{1}, {u}_{2}, {u}_{3})$       659
Confluent hypergeometric, equation      297
Confluent hypergeometric, function (series)      297
Confluent hypergeometric, function (series), zeros      424
Conical, coordinates      662
Conical, functions      294
Converge in mean      38
Curvilinear coordinate system $({u}_{1}, {u}_{2}, {u}_{3})$ of a vector v      659
Cylinder function      368 398 401 422 428 431 432 438
Cylindrical coordinates      659
Darboux formula      8
Deficiency      490
Degree of the LamЈ function      594
Dini expansion      454
Dirichlet integral      106
Double rational transformation      491
Double-parameter eigenvalue problem      616
Doubly-periodic function      462
Duplication formula, for $\varphi$       483
Duplication formula, for $\vartheta$       505
Duplication formula, for Jacobian elliptic function      539
Duplication formula, tor E(u),Z(u)      558
Eigenvalue      616
Ellipsoidal, coordinates      575 576 664
Ellipsoidal, harmonics      589
Ellipsoidal, harmonics, first species (first case of the second species)      590 606
Ellipsoidal, harmonics, four species      590
Ellipsoidal, harmonics, fourth species      591 606
Ellipsoidal, harmonics, second species      590
Ellipsoidal, harmonics, second species, second case      606
Ellipsoidal, harmonics, second species, third case      606
Ellipsoidal, harmonics, third species      590 606
Ellipsoidal, integral representation      604
Elliptic function      462
Elliptic function, general theory      462
Elliptic integral , first kind      460
Elliptic integral , general form      456
Elliptic integral , periods      461
Elliptic integral , periods, second kind      552 642
Elliptic integral , periods, third kind      553 572
Elliptical cylinder coordinates      660
Equation of Fuchsian type      64
Equation of Laplacian type      335 352
Error function erf x      333
Euler constant      12 98
Euler numbers      6
Euler polynomials      5
Euler product of the $\zeta$ -function      123
Euler transform      85 92
Euler's infinite product expression of $\Gamma$ -function      97
Euler's integral, first kind      103
Euler's integral, second kind      93
Euler-Maclanrin formula      8
Exponential integral ${E}_{n}(x)$       334
Expressions for the complete elliptic integrals of the third kind      555
Finite representations of ${Q}_{n}(x)$       226
Flotmet solution      614 638
Flotmet solution, characteristic exponents      635
Flotmet solution, Fourier expansion      618
Flotmet solution, half-period      615
Flotmet solution, whole-period      615
Fourier coefficients generalised      38
Frobenius method      61
Fundamental elliptic integrals      457 458
Fundamental elliptic integrals, three      545
Fundamental recurrence relations of the Bessel functions      350
Gamma function      93
Gegenbauer, addition formula      397
Gegenbauer, expansion      452
Gegenbauer, function ${C}_{\alpha}^{\lambda}(z)$       291
Gegenbauer, polynomial      274 398 401 427 432
Generating function, ${C}_{n}^{\lambda}(cos\theta)$       290
Generating function, ${D}_{n}(z)$       323
Generating function, ${J}_{n}(z)$       359 360
Generating function, ${L}_{\n}^{\mu}(z)$       328
Generating function, Bessel functions of order half an odd integer      431
Generating function, Legendre polynomials      216
Genus      490
Glaisher's symbols      532
Graf formula      396
Half-period solution      615 622 624 626
Hankel, functions first and second kind      369
Hankel, integral formula      402
Hardy formula      448

Hermite, equation      76 325
Hermite, formula      120
Hermite, function      326
Hermite, polynomial      77 326
Hermite, polynomial, derivative expression      326
Heun equation      608
Hill equation      612
Hill equation, general      633
Hyper-elliptic integral      456
Hypergeometric equation      135
Hypergeometric function      137
Hypergeometric function, analytic continuation formulae      162
Hypergeometric function, Barnes' integral representation      156
Hypergeometric polynomial of degree n      169
Hypergeometric series      136
Hypergeometric series, generalised      189 411
Imaginary modulus transformation      544
Imaginary transformation      555 556 564
Imaginary transformation, Jacobi      562
Incomplete Gamma function $\gamma(n,x)$       333
Indicial equation      58
Inequalities about ${J}_{n}(z)$       364
Infinite product      21
Infinite product, absolute convergence      23
Infinite product, uniform convergence      25
Inner product      36
Integral (entire) function      25
Integral (entire) function, prime factor of      25
Integral representation      226 369
Integral representation, ${J}_{n}(z)$       364
Integral representation, ${J}_{\nu}(z)$       351
Integrals containing Bessel functions      399 401
Inversion of an elliptic integral      462
Jacobi, imaginary transformation      516 542
Jacobi, polynomial      168 173 215
Jacobi, polynomial, asymptotic expression      206
Jacobi, polynomial, degree n      169
Jacobi, polynomial, degree n, generating function      171
Jacobi, transformation formula      426
Jacobian elliptic function      459 530
Jacobian elliptic function, periodicity      539
Jacobian elliptic function, seros and poles      540
Kapteyn, expansion      415 419
Kapteyn, expansion, ${(t-z)}^{-1}$       419
Kapteyn, expansion, ${z}^{n}$       416
Kapteyn, expansion, general      453
Kapteyn, expansion, general analytic function      420
Kapteyn, polynomials      420
Kapteyn, series      416
Kepler equation      415
Kernel, Euler transform      80
Kernel, integral transform      79
Kernel, Laplace transform      80
Kernel, Mellin transform      80
Kummer, equation      297 347
Kummer, formula      130 184
Kummer, formula, first      298
Kummer, formula, second      299 335
Kummer, function      297
Kummer, transformation      298
Lagrange, expansion formula      15 388
Lagrange, formula      384
Laguerre polynomial      327
Laguerre polynomial, generalised ${L}_{n}^{\mu}(z)$       327
Lame, equation      67 88 580 581
Lame, equation, generalized      67 88
Lame, functions      575 581
Lame, functions, degree      595
Lame, functions, degree, first type (first kind)      584 597 603
Lame, functions, degree, four groups      589
Lame, functions, degree, four types      583
Lame, functions, degree, fourth group      604
Lame, functions, degree, fourth type      586 604
Lame, functions, generalized      599
Lame, functions, integral equations      602
Lame, functions, periodic      599
Lame, functions, periodic, second kind      597
Lame, functions, periodic, second type      585 603
Lame, functions, periodic, third type      585 603
Lame, functions, zeros      589
Lame, Jacobian form      582
Lame, polynomials zeros      595
Lame, Weierstrass' form      582
Laplace, first integral representation of ${P}_{\nu}(x),$       263
Laplace, integral      34
Laplace, integral, representation of ${P}_{n}(x),$ first      217
Laplace, integral, representation of ${P}_{n}(x),$ second      218
Laplace, second integral representation of ${P}_{\nu}(x),$       263
Laplace, series      246
Laplace, tranform      34 81
Laplace, tranform, convolution theorem      338
Laplacian operator in curvilinear coordinates      658
Legendre, elliptic integral, first kind      510 530
Legendre, elliptic integral, second kind      552
Legendre, elliptic integral, third kind      553
Legendre, equation      67. 210
Legendre, function      210
Legendre, function, first kind      434
Legendre, function, first kind, degree $\nu$       250
Legendre, function, integral representation      226
Legendre, function, second kind      225 434
Legendre, polynomials      212 398 399 427
Legendre, relation      557 566
Legendre, series      222
Legendre, standard form      548
Lerch transformation formula      133
Logarithmic, derivation of $\Gamma$ -function      107
Logarithmic, integral       334
Magnus addition formula      339
Mathieu, equation      67 610
Mathieu, equation, periodic solution      624
Mathieu, functions      610
Mathieu, functions, expansion formulae      646
Mathieu, functions, Fourier coefficients      645
Mathieu, functions, integral equation      644
Mathieu, functions, modified      651
Mehler-Dirichlet integral representation of ${P}_{\nu}(cos\theta)      264
Meromorphic function      17
Method of steepest descent      381
Mittag-Leffler theorem      17
Modified (or Imaginary Argument) Bessel function      374
Modified (or Imaginary Argument) Bessel function, first kind      374
Modified (or Imaginary Argument) Bessel function, second kind      374
Modulus      511
Moebius function      134
Multiplied solution      53
Murphy's expression ${P}_{n}(x)$       214 215
Neumann, expansion      232 412 419
Neumann, expansion, analytic function      414
Neumann, expression for ${Q}_{n}(x)$       227
Neumann, formula      401
Neumann, functions      366
Neumann, integral formula      432
Neumann, polynomial      413 451 455
Neumann, polynomial, second kind      451
Niven's, expression      605
Niven's, representation      591
Norm      39
Normal solutions      73
Normalization      624
Order, elliptic function      463
Order, of equation and of the solutions      345
Ordinary point      48
Orthogonal curvilinear coordinates      577
Orthogonal curvilinear coordinates, systems      658
Orthogonality, condition      577
Orthogonality, relations      627
Orthogonality, relations, Bessel functions      424
Orthonormal relations      424
Orthonormal system(set)      36

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