bounded%20variation

SearchAdvancedHelp

(0.002 seconds)

1—10 of 200 matching pages

1: 10.17 Asymptotic Expansions for Large Argument

… ►

§10.17(iii) Error Bounds for Real Argument and Order

… ►

§10.17(iv) Error Bounds for Complex Argument and Order

… ►Bounds for ${𝒱}_{z,\mathrm{i}\mathrm{\infty }}\left(t^{-\mathrm{\ell }}\right)$ are given by … ►The bounds (10.17.15) also apply to ${𝒱}_{z,-\mathrm{i}\mathrm{\infty }}\left(t^{-\mathrm{\ell }}\right)$ in the conjugate sectors. Corresponding error bounds for (10.17.3) and (10.17.4) are obtainable by combining (10.17.13) and (10.17.14) with (10.4.4). …

2: 10.40 Asymptotic Expansions for Large Argument

… ►

§10.40(ii) Error Bounds for Real Argument and Order

… ►

§10.40(iii) Error Bounds for Complex Argument and Order

… ►where $𝒱$ denotes the variational operator (§2.3(i)), and the paths of variation are subject to the condition that $|\mathrm{\Re }t|$ changes monotonically. Bounds for ${𝒱}_{z,\mathrm{\infty }}\left(t^{-\mathrm{\ell }}\right)$ are given by … ►If $z\to \mathrm{\infty }$ with $|\mathrm{\ell }-2|z||$ bounded and $m$ $(\ge 0)$ fixed, then …

3: Bibliography Y

… ►

Simple Variational Proof That Any Two-Dimensional Potential Well Supports at Least One Bound State. American Journal of Physics 57 (1), pp. 85–86.

ⓘ

External Links:

Document

Referenced by:

§1.18(viii).

Encodings:

BibTeX

…

4: 1.4 Calculus of One Variable

… ►

Functions of Bounded Variation

… ►If , then $f(x)$ is of bounded variation on $(a,b)$. In this case, $g(x)={𝒱}_{a,x}\left(f\right)$ and $h(x)={𝒱}_{a,x}\left(f\right)-f(x)$ are nondecreasing bounded functions and $f(x)=g(x)-h(x)$. … ►For further information on total variation see Olver (1997b, pp. 27–29). …

5: Bibliography N

… ►

Error bounds for the asymptotic expansion of the Hurwitz zeta function. Proc. A. 473 (2203), pp. 20170363, 16.

ⓘ

External Links:

ISSN 1364-5021, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§8.15.

Encodings:

BibTeX

… ►

Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function. Appl. Anal. Discrete Math. 7 (1), pp. 161–179.

ⓘ

External Links:

ISSN 1452-8630, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§5.11(ii), §5.11(ii).

Encodings:

BibTeX

… ►

Error bounds and exponential improvement for the asymptotic expansion of the Barnes $G$-function. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2172), pp. 20140534, 14.

ⓘ

External Links:

ISSN 1364-5021, MathReview (Mehdi Hassani), ZentralBlatt

Referenced by:

§5.17, §5.17.

Encodings:

BibTeX

… ►

Bounds for symmetric elliptic integrals. J. Approx. Theory 122 (2), pp. 249–259.

ⓘ

External Links:

ISSN 0021-9045, Document, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§19.24(ii), §19.24(i), §19.9(i).

Encodings:

BibTeX

… ►

Inequalities and bounds for the incomplete gamma function. Results Math. 63 (3-4), pp. 1209–1214.

ⓘ

External Links:

ISSN 1422-6383, Document, FullText, MathReview (Pierpaolo Natalini), ZentralBlatt

Referenced by:

§8.10, §8.10.

Encodings:

BibTeX

…

6: Bibliography P

… ►

Error bounds for the uniform asymptotic expansion of the incomplete gamma function. J. Comput. Appl. Math. 147 (1), pp. 215–231.

ⓘ

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§8.12.

Encodings:

BibTeX

… ►

Variational approach to excitons in carbon nanotubes. Phys. Rev. B 67 (7), pp. (073401–1)–(073401–4).

ⓘ

External Links:

Document

Referenced by:

§11.12.

Encodings:

BibTeX

… ►

Bounds for ratios of modified Bessel functions. Integral Transform. Spec. Funct. 9 (4), pp. 293–298.

ⓘ

External Links:

ISSN 1065-2469, Document, MathReview, ZentralBlatt

Referenced by:

§10.37.

Encodings:

BibTeX

… ►

Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

ⓘ

Notes:

Double-precision Fortran, maximum accuracy 20S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

6th item.

Encodings:

BibTeX

…

7: Bibliography S

… ►

On Lindelöf’s error bound for Stirling’s series. J. Reine Angew. Math. 404, pp. 135–139.

ⓘ

External Links:

ISSN 0075-4102, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§5.11(ii).

Encodings:

BibTeX

… ►

Variational calculations of scattering. Ann. Phys. 16, pp. 36–50.

ⓘ

Referenced by:

§18.39(iv).

Encodings:

BibTeX

… ►

Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros. Math. Comp. 70 (235), pp. 1205–1220.

ⓘ

External Links:

ISSN 0025-5718, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.74(vi).

Encodings:

BibTeX

… ►

Bounds for ratios of modified Bessel functions and associated Turán-type inequalities. J. Math. Anal. Appl. 374 (2), pp. 516–528.

ⓘ

External Links:

ISSN 0022-247X, Document, FullText, MathReview (Beyza Caliskan Aslan), ZentralBlatt

Referenced by:

§10.37, §10.37.

Encodings:

BibTeX

… ►

The Bound State of Weakly Coupled Schrödinger Operators in One and Two Dimensions. Annals of Physics 97 (2), pp. 279–288.

ⓘ

External Links:

Document, MathReview Entry

Referenced by:

§1.18(viii).

Encodings:

BibTeX

…

8: Bibliography M

… ►

Table of the ratio: Area to bounding ordinate, for any portion of normal curve. Biometrika 18, pp. 395–400.

ⓘ

External Links:

FullText, ZentralBlatt

Referenced by:

§7.8.

Encodings:

BibTeX

… ►

New sharp bounds for gamma and digamma functions. An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 57 (1), pp. 57–60.

ⓘ

External Links:

ISSN 1221-8421, Document, MathReview (Daniele Ritelli), ZentralBlatt

Referenced by:

§5.6(i).

Encodings:

BibTeX

… ►

Further improvements of some double inequalities for bounding the gamma function. Math. Comput. Modelling 57 (5-6), pp. 1360–1363.

ⓘ

External Links:

ISSN 0895-7177, Document, FullText, MathReview (Emil C. Popa)

Referenced by:

§5.6(i).

Encodings:

BibTeX

… ►

Latent roots and matrix variates: A review of some asymptotic results. Ann. Statist. 6 (1), pp. 5–33.

ⓘ

External Links:

FullText, MathReview (Yasuko Chikuse), ZentralBlatt

Referenced by:

§35.6(i), §35.6(iii).

Encodings:

BibTeX

… ►

The variation with respect to order of zeros of Bessel functions. Rend. Sem. Mat. Univ. Politec. Torino 39 (2), pp. 15–25.

ⓘ

External Links:

MathReview (S. Ahmed), ZentralBlatt

Referenced by:

§10.21(iv).

Encodings:

BibTeX

…

9: 18.39 Applications in the Physical Sciences

… ►The non-relativistic Schrödinger equation describing a single, bound (negative energy) electron, in an $L^2$ eigenstate of energy $E$ is: … ►These, taken together with the infinite sets of bound states for each $l$, form complete sets. … ►While $s$ in the basis of (18.39.44) is simply a variational parameter, care must be taken, or the relationship between the results of the matrix variational approximation and the Pollaczek polynomials is lost, although this has no effect on the use of the variational approximations Reinhardt (2021a, b). … ►which is Bohr’s quantization for the Coulomb bound state energies (18.39.31). … ►For applications and an extension of the Szegő–Szász inequality (18.14.20) for Legendre polynomials ($\alpha =\beta =0$) to obtain global bounds on the variation of the phase of an elastic scattering amplitude, see Cornille and Martin (1972, 1974). …

10: Bibliography O

… ►

Error bounds for asymptotic expansions in turning-point problems. J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.

ⓘ

External Links:

Document, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§2.8(iii).

Encodings:

BibTeX

… ►

Bounds for the solutions of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B (4), pp. 161–166.

ⓘ

External Links:

MathReview (C. W. Clenshaw), ZentralBlatt

Referenced by:

§2.9(i).

Encodings:

BibTeX

… ►

Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.

ⓘ

Notes:

See also Olver (1997b)

External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§2.3(iv).

Encodings:

BibTeX

… ►

Improved error bounds for second-order differential equations with two turning points. J. Res. Nat. Bur. Standards Sect. B 80B (4), pp. 437–440.

ⓘ

External Links:

MathReview (Peter Deuflhard), ZentralBlatt

Referenced by:

§2.8(vi).

Encodings:

BibTeX

… ►

Asymptotic approximations and error bounds. SIAM Rev. 22 (2), pp. 188–203.

ⓘ

External Links:

ISSN 0036-1445, Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§2.7(iii).

Encodings:

BibTeX

…