integral%20representation%20of%20solutions

SearchAdvancedHelp

(0.002 seconds)

10 matching pages

1: Bibliography V

… ►

Representation of Lie Groups and Special Functions. Volume 1: Simplest Lie Groups, Special Functions and Integral Transforms. Mathematics and its Applications (Soviet Series), Vol. 72, Kluwer Academic Publishers Group, Dordrecht.

ⓘ

Notes:

Translated from the Russian by V. A. Groza and A. A. Groza

External Links:

ISBN 0-7923-1466-2, MathReview (Robert A. Gustafson), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

… ►

Representation of Lie Groups and Special Functions. Volume 2: Class I Representations, Special Functions, and Integral Transforms. Mathematics and its Applications (Soviet Series), Vol. 74, Kluwer Academic Publishers Group, Dordrecht.

ⓘ

Notes:

Translated from the Russian by V. A. Groza and A. A. Groza

External Links:

ISBN 0-7923-1492-1, MathReview (P. D. F. Ion), ZentralBlatt

Referenced by:

§18.38(iii).

Encodings:

BibTeX

►

Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

§13.27.

Encodings:

BibTeX

… ►

Integral representations for products of Lamé functions by use of fundamental solutions. SIAM J. Math. Anal. 15 (3), pp. 559–569.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (F. M. Arscott), ZentralBlatt

Referenced by:

§29.8.

Encodings:

BibTeX

… ►

Fourier series representation of Ferrers function $𝖯$ .

ⓘ

External Links:

FullText

Referenced by:

(14.13.1).

Encodings:

BibTeX

…

2: 36.5 Stokes Sets

… ►

§36.5(ii) Cuspoids

… ►For , there are two solutions $u$, provided that $|Y|>{(\frac{2}{5})}^{1/2}$. … ►The first sheet corresponds to and is generated as a solution of Equations (36.5.6)–(36.5.9). … ►

§36.5(iii) Umbilics

… ►

§36.5(iv) Visualizations

…

3: Bibliography C

… ►

On the representation of a large even integer as the sum of a prime and the product of at most two primes. Kexue Tongbao (Foreign Lang. Ed.) 17, pp. 385–386.

ⓘ

External Links:

MathReview (T. Hayashida)

Referenced by:

§27.13(ii).

Encodings:

BibTeX

… ►

On a Tricomi series representation for the generalized exponential integral. Internat. J. Comput. Math. 31, pp. 257–262.

ⓘ

Notes:

Includes Fortran code

External Links:

Document, ZentralBlatt

Referenced by:

§8.28(vi).

Encodings:

BibTeX

… ►

On some series representations of the Hurwitz zeta function. J. Comput. Appl. Math. 216 (1), pp. 297–305.

ⓘ

External Links:

ISSN 0377-0427, Document, FullText, MathReview, ZentralBlatt

Referenced by:

§25.11(iv), §25.11(iv).

Encodings:

BibTeX

… ►

Multi-Integral Representations for Associated Legendre and Ferrers Functions. Symmetry 12 (10).

ⓘ

External Links:

Link, ISSN 2073-8994, Document, ZentralBlatt

Referenced by:

§14.6(ii), §14.6(ii), Erratum (V1.1.1) for Subsection 14.6(ii).

Encodings:

BibTeX

… ►

On parameter differentiation for integral representations of associated Legendre functions. SIGMA Symmetry Integrability Geom. Methods Appl. 7, pp. Paper 050, 16.

ⓘ

External Links:

ISSN 1815-0659, Document, FullText, MathReview (Michael Doschoris), ZentralBlatt

Referenced by:

§14.11, §14.11.

Encodings:

BibTeX

…

4: Bibliography R

… ►

A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.

ⓘ

External Links:

ISSN 0008-414X, Document, Link, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.18(v).

Encodings:

BibTeX

… ►

On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

ⓘ

External Links:

ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

Referenced by:

§16.4(iii), §16.4(iii).

Encodings:

BibTeX

… ►

Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.

ⓘ

External Links:

ISSN 0044-2275, Document, MathReview (P. K. Banerji), ZentralBlatt

Referenced by:

§9.11(iii), §9.11(v), §9.11(v), (9.5.6), §9.5(ii).

Encodings:

BibTeX

►

Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.

ⓘ

External Links:

ISSN 0044-2275, Document, MathReview (E. R. Love), ZentralBlatt

Referenced by:

(9.11.16), (9.11.17), §9.11(iii), §9.11(v).

Encodings:

BibTeX

►

Integral representations for products of Airy functions. III. Quartic products. Z. Angew. Math. Phys. 48 (4), pp. 656–664.

ⓘ

External Links:

ISSN 0044-2275, Document, MathReview (E. R. Love), ZentralBlatt

Referenced by:

§9.11(iii), §9.11(v).

Encodings:

BibTeX

…

5: Bibliography M

… ►

Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.

ⓘ

Notes:

Includes Fortran code, maximum accuracy 20S.

External Links:

ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§6.13, 4th item, §6.21(ii).

Encodings:

BibTeX

… ►

An integral representation for the Bessel form. J. Comput. Appl. Math. 57 (1-2), pp. 251–260.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview (Hans-Jürgen Glaeske), ZentralBlatt

Referenced by:

§18.34(ii).

Encodings:

BibTeX

… ►

An integral representation for the Lambert $W$ function.

ⓘ

External Links:

2012.02480

Referenced by:

(4.13.16), §4.13.

Encodings:

BibTeX

… ►

The Airy Integral, Giving Tables of Solutions of the Differential Equation $y^{\prime \prime }=xy$ . British Association for the Advancement of Science, Mathematical Tables Part-Vol. B, Cambridge University Press, Cambridge.

ⓘ

External Links:

MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

1st item, 1st item, §9.2(i), §9.2(ii), §9.2(v), §9.4, (9.6.2), (9.6.3), (9.6.4), (9.6.5), (9.6.6), (9.6.7), (9.6.8), (9.6.9), §9.6(i), §9.8(i), §9.8(ii), §9.8(iv), §9.9(ii), Ch.9.

Encodings:

BibTeX

… ►

The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

ⓘ

External Links:

ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§18.27(v).

Encodings:

BibTeX

…

6: Bibliography G

… ►

The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals. Ann. of Math. (2) 48 (4), pp. 785–826.

ⓘ

External Links:

FullText, MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§35.2, §35.3(ii).

Encodings:

BibTeX

… ►

Integral representations for computing real parabolic cylinder functions. Numer. Math. 98 (1), pp. 105–134.

ⓘ

External Links:

ISSN 0029-599X, Document, MathReview Entry, ZentralBlatt

Referenced by:

§12.18.

Encodings:

BibTeX

… ►

Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

ⓘ

Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

Referenced by:

3rd item, §10.77(ix).

Encodings:

BibTeX

… ►

Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.

ⓘ

External Links:

FullText, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§26.1, §26.1, Notations S, Notations S.

Encodings:

BibTeX

… ►

Representations of Integers as Sums of Squares. Springer-Verlag, New York.

ⓘ

External Links:

ISBN 0-387-96126-7, MathReview (Harvey Cohn), ZentralBlatt

Referenced by:

§27.13(iv).

Encodings:

BibTeX

…

7: Bibliography S

… ►

The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions. 2nd edition, Graduate Texts in Mathematics, Vol. 203, Springer-Verlag, New York.

ⓘ

Notes:

First edition published by Wadsworth & Brooks/Cole Advanced Books & Software, 1991.

External Links:

ISBN 0-387-95067-2, MathReview, ZentralBlatt

Referenced by:

§26.19.

Encodings:

BibTeX

… ►

On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt

Referenced by:

§29.17(i), §29.8.

Encodings:

BibTeX

… ►

On integral representation of Weber’s parabolic cylinder function and its expansion into an infinite series. J. Indian Math. Soc. (N. S.) 4, pp. 34–38.

ⓘ

External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

Encodings:

BibTeX

… ►

Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

ⓘ

External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

Encodings:

BibTeX

… ►

Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill. Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.

ⓘ

External Links:

ZentralBlatt

Referenced by:

§28.8(ii).

Encodings:

BibTeX

…

8: Bibliography K

… ►

Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.

ⓘ

External Links:

Document, MathReview (Matti Jutila), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

… ►

Closed-form representations of the Lambert $W$ function. Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.

ⓘ

External Links:

ISSN 1311-0454, MathReview (Lewis H. Ryder), ZentralBlatt

Referenced by:

§4.13.

Encodings:

BibTeX

… ►

Rational solutions of the fifth Painlevé equation. Differential Integral Equations 7 (3-4), pp. 967–1000.

ⓘ

External Links:

ISSN 0893-4983, MathReview, ZentralBlatt

Referenced by:

§32.8(v).

Encodings:

BibTeX

►

Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

ⓘ

External Links:

ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX

…

9: Bibliography B

… ►

Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

ⓘ

External Links:

Document

Referenced by:

§33.22(iv).

Encodings:

BibTeX

… ►

Integral representations and summations of the modified Struve function. Acta Math. Hungar. 141 (3), pp. 254–281.

ⓘ

External Links:

ISSN 0236-5294, Document, FullText, MathReview (Eugenia N. Petropoulou), ZentralBlatt

Referenced by:

§11.7(v), §11.7(v).

Encodings:

BibTeX

… ►

Integral equations and exact solutions for the fourth Painlevé equation. Proc. Roy. Soc. London Ser. A 437, pp. 1–24.

ⓘ

External Links:

ISSN 0962-8444, FullText, MathReview (Mehmet Can), ZentralBlatt

Referenced by:

§32.11(v), §32.2(iii).

Encodings:

BibTeX

… ►

Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

Encodings:

BibTeX

… ►

Riemann zeta function: Rapidly converging series and integral representations. Appl. Math. Lett. 5 (2), pp. 83–88.

ⓘ

External Links:

ISSN 0893-9659, Document, MathReview (Jacek Fabrykowski), ZentralBlatt

Referenced by:

§25.18(i).

Encodings:

BibTeX

…

10: 18.39 Applications in the Physical Sciences

… ►The solutions (18.39.8) are called the stationary states as separation of variables in (18.39.9) yields solutions of form … ►Brief mention of non-unit normalized solutions in the case of mixed spectra appear, but as these solutions are not OP’s details appear elsewhere, as referenced. … ►The technique to accomplish this follows the DVR idea, in which methods are based on finding tridiagonal representations of the co-ordinate, $x$. Here tridiagonal representations of simple Schrödinger operators play a similar role. … ►The Coulomb–Pollaczek polynomials provide alternate representations of the positive energy Coulomb wave functions of Chapter 33. …