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Chaudhry M.A., Zubair S.M. — On a Class of Incomplete Gamma Functions with Applications
Chaudhry M.A., Zubair S.M. — On a Class of Incomplete Gamma Functions with Applications



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Название: On a Class of Incomplete Gamma Functions with Applications

Авторы: Chaudhry M.A., Zubair S.M.

Аннотация:

The subject of special functions is rich and expanding continuously with the emergence of new problems encountered in engineering and applied science applications. The development of computational techniques and the rapid growth in computing power have increased the importance of the special functions and their formulae for analytic representations. However, problems remain, particularly in heat conduction, astrophysics, and probability theory, whose solutions seem to defy even the most general classes of special functions.On a Class of Incomplete Gamma Functions with Applications introduces a class of special functions, developed by the authors, useful in the analytic study of several heat conduction problems. It presents some basic properties of these functions, including their recurrence relations, special cases, asymptotic representations, and integral transform relationships. The authors explore applications of these generalized functions to problems in transient heat conduction, special cases of laser sources, and problems associated with heat transfer in human tissues. They also discuss applications to astrophysics, probability theory, and other problems in theory of functions and present a fundamental solution to time-dependent laser sources with convective-type boundary conditions. Appendices include an introduction to heat conduction, Fourier conduction, a table of Laplace transforms, and well-known results regarding the improper integrals. Filled with tabular and graphical representations for applications, this monograph offers a unique opportunity to add to your mathematical toolbox a new and useful class of special functions.


Язык: en

Рубрика: Математика/Анализ/Специальные функции/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 492

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(a;q)_n$      31
$(a;q)_{\infty}$      31
$(\alpha)_n$      6
$B(x, y;b)      221
$ber_{\nu}(z)$      275
$B_n$      288
$B_n(x)$      288
$B_q(x,y)      31
$B_x($\nu,\mu)$      217
$C(\alpha)$      305
$C_t(\nu, b)$      42
$C_{e^2_{\mu,\nu}}(a,z)$      60
$C_{e_{\mu,\nu}}(a,z)$      62
$C_{e_{\mu}}(a,z)$      62
$C_{\Gamma}(\alpha, x;\omega)$      142
$C_{\Gamma}(\alpha, x;\omega;s)$      146
$daw(\sqrt{x})$      38
$D_{\alpha}(z)$      271
$E_t(\nu,a)$      41
$E_{\alpha,\beta}(z)$      276
$f(u)$      151
$F(z,\alpha)$      07
$f_B(t;\alpha,\beta)$      220
$f_m(z)$      266
$H_{p,q}^{m,n}$      81
$I(\alpha,q)$      307
$I(\alpha;\nu;s;b)$      75
$I_b(\alpha,q)$      312
$I_b^*(\alpha,q)$      312
$I_{\nu}(z)$      67 274
$J_{a,b}(y;f;g)$      455
$J_{\alpha}(z)$      86
$J_{\nu}\(z)$      274
$J_{\nu}^{\mu}(z)$      276
$K_{e^2_{\mu.\nu}}(a, z)$      60
$K_{\nu}(z)$      196
$L_n^{\mu}(x)$      81
$S_t(\nu,b)$      42
$S_{\Gamma}(\alpha, x;\omega)$      142
$S_{\Gamma}(\alpha, x;\omega;s)$      146
$W_{\lambda,\mu}$      20
$\gamma$      4
$\Gamma(\alpha)$      1
$\Gamma(\alpha, x;b)$      43
$\Gamma(\alpha, x;b;\beta)$      266
$\gamma(\alpha,x;b)$      43
$\gamma(\alpha,x;b;\beta)$      266
$\Gamma_2(\beta,\beta',x,y)$      57
$\Gamma_b(\alpha)$      9
$\Gamma_q(x)$      31
$\Gamma_{p,q}^{m,n}\left((z,x)\right)$      283
$\Gamma_{\nu}(\alpha, x;b)$      282
$\gamma_{\nu}(\alpha,x;b\)$      196
$\Phi(a;b;z)$      38
$\pi(x)$      290
$\psi(z)$      20
$\psi_b(\alpha)$      24
$\zeta(\alpha)$      290 296
$\zeta(\alpha,q)$      306
$\zeta_b(\alpha)$      298
$\zeta_b(\alpha,q)$      308
$\zeta_b^*(\alpha)$      304
$\zeta_b^*(\alpha,q)$      309
$_0F_{\beta}$      273
$_p\psi_q$      281
A(a, b)      7
Abelian theorems      448
Abel’s Test      458
Ablating boundary      385
Ablation      329
Abramowitz’s function      265 266 271
Absorbed      329
Absorption      329
Absorption coefficient      386 410
Adiabatic      443
Affine transformation      445
Agrest and Maksimov      62
Alloy      346
Alzer      8 22 23
Amplitude      366 379 381
Analytic continuation      31 39 293
Analytic formulation      416
Analytic Theorem      449
Anderson      23 267
Antenna theory      134
Apple transformation      446
Applied mathematics      37
Arbitrary function      445
Arc welding      415
Argument reflection formula      218
Argument-addition and argument-multiplication formulas      289
Arithmetic and quadratic mean      7
Arithmetic mean      12
Astrophysical thermonuclear functions      267
Astrophysics      37 41
Astrophysics and space sciences      268
Asymptotic behavior      39
Asymptotic expansion      80
Asymptotic expansion for the digamma function      22
Asymptotic formula for the gamma function      6
Asymptotic property      82
Asymptotic representation      18 80 129 132 218 277 303 304 306
Asymptotic value      383
Auxiliary layer      444
Auxiliary problem      358 372
Axisymmetric problems      75
Backlund      297
Barndorff — Nielsen      195
Barnes      280
Bateman function      219
Beam      415
bei(z)      275
ber(z)      275
Berg      32
Berg and Forst      19
bernoulli      320
Bernoulli numbers      22 287 304
Bernoulli polynomials      7 289
Bessel functions      138
beta function      215
Beta probability distribution      220
Beta random variables      220
BINARY      343
Binet      21 24
Binomial coefficient      216
Biot      385
Blackwell      385 386 398 400
Bohmer      37
Bohmer integrals      136
Boundary condition      330 342 345 346 353 358 372 378 416 417 444
Brazing      329
Brent      298
Brownian motion      195
BSKS      89
Bulk temperature      330
Buoyancy force      330 338
Busbridge      132
Bushman      271
C. Fox      280
Cancerous cell      381
Capillary      339 343 345
Carslaw      360 363 366 378 394 416
Carslaw and Jaeger      152
Casting      329
Cauchy integral theorem      294
Cauchy — Saalschiitz representations      2
Cauchy’s Theorem      32
cell      381
Change-of-phase      329
Chaudhry      334 357 385 389 402 416
Chemical      415 441
Chi-square      196
Circular frequency      443
Classical      334
Claussen      415
Clockwise direction      313
Closed-form      329 330 334 359 373 416
Complementary error function      361 376 420 421 444
Completely monotonic      19
COMPLEX      444
Condensation process      415
Conduction equation      347 417 418
Confluent hypergeometric function      38 53 81 86
Continuous analogue      309
Continuous casting      415
Contour $L_+(p)$      294
Contour integral      307
Contour integral representation      215
Contour Plot      421 428
Control volume      442
Controlling factor      363 366 377 379 381
Controlling parameter      370 381 425 432 439
Convection      334
Convection coefficient      400
Convection heat transfer      443
Convective boundary condition      334 385 397
Convexity      7
Convolution      47 446
Cornu’s spiral      135 136
Critical      383
Cryosurgery      339
Crystal      347
Crystal growth processes      151
Cumulative density function      19 44 129 196 221 266
Curvature      135
Cutting tool      419
Cvijovic      319
Cylindrical coordinate      343 418
Cylindrical symmetry      43 346 418
Dabby      385
Dawson integral function      125 265 267
De La Vallee Poussin      298
Decomposition      416 424 432 438
Decomposition formula      37 126 152 197 269
Decomposition theorem      45
Decompositions of the Fox H-functions      265
Del operator      441
Demographic rates      195 196
Dendrite      343
density      442
Die      329
Difference equation      7
Difference formula      10
Differential equation      330 345 346 417 441 443
Differential formulation      370
Differential representations      210
Differentiation formula      53 360 365 374 405
Diffraction      37
Diffraction theory      134
Diffusion effect      392
Digamma Function $\psi(x)$      20
Dimensional analysis      334
Dimensional parameter      334
Dimensionless      392 420
Dimensionless form      406 428 435
Dimensionless parameter      342 347 397 398 400 408 420 424 425 428 431 432 435 438 439
Dimensionless subcooling      331
Dimensionless temperature      337 342 346 353 400 421
Dimensionless time      361 374 433
Dimensionless variable      365 374 376 378 389 390 396 406
Directional solidification      329
Dirichlet      24 25
Dirichlet series      293
Dirt      347
Divergence theorem      442
Dixon      280
Duhamel      358 359 370 372
e function      353
e(u)      151
E(u,v)      149
Earth’s crust      143
Efro’s Theorem      450
El-Adawi      413
Electric      329 443
Electrical      441
Electrical conductor      415
Electrical network      334
Elementary function      435 439
Elementary transcendental function      15
Energetic      441
Energy absorption      390 406
Energy balance      338 345
Energy deposition      397
energy equation      354
Energy flux      410
Energy source      397
Engineering material      415 416
Enthalpy function      354
Enthalpy method      354
Erlang      196
Error functions      82 124 126 417
Euclid      292
Euler gamma function      32
Eulerian integral of the first kind      215
Euler’s constant      4
Euler’s integral of the first kind      217
Eutectic alloy      343
Even or odd symmetry      289
Exact formulation      415
Excess temperature      410
Explicit      334
Exponential function      376
Exponential integral function      131 267 342
Exponential solution      444
Exponential type      363 373 376 419 424 427 431 435 438
Exposed surface      385
Extended beta function      13 14 221
Extended cosine and sine decompositions      148
Extended gamma functions      265
Extended Hurwitz formulae      311
Extended incomplete gamma functions      266
Extended range      354
Extended sine and cosine decomposition functions      146
Extended zeta function      298 304
Extended zone      343
f function      353
F(u,v)      149
Factorials      2
Fermat numbers      292
Ferrar      280
Film coefficient      443
Final value theorem      450
Finite difference      354
Finite element      354
First kind      443 444
First law      442
First shape factor      220
Fixed grid      354
Flame hardening      415
Flat plate      418
Flow effect      330
Forestry      196
FORM      329
FOURIER      385
Fourier cosine and sine transforms      149
Fourier cosine transform      141
Fourier kernel      280
Fourier number      361 402
Fourier sine transform      141
Fourier transform operator      302
1 2 3
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