Bailey 4F3(1) sum

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11: Bibliography

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Transformations $R{S}_4^2(3)$ of the ranks $\le 4$ and algebraic solutions of the sixth Painlevé equation. Comm. Math. Phys. 228 (1), pp. 151–176.

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ISSN 0010-3616, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

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§32.9(iii).

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A trinomial analogue of Bailey’s lemma and $N=2$ superconformal invariance. Comm. Math. Phys. 192 (2), pp. 245–260.

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ISSN 0010-3616, Document, MathReview (Anne Schilling), ZentralBlatt

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§17.12.

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Congruences for the $q$-secant numbers. European J. Combin. 1 (4), pp. 283–287.

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ISSN 0195-6698, MathReview (J. E. Cigler), ZentralBlatt

Referenced by:

§24.16(iii).

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Umbral calculus, Bailey chains, and pentagonal number theorems. J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.

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Notes:

In memory of Gian-Carlo Rota

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ISSN 0097-3165, Document, MathReview (Alessandro Di Bucchianico), ZentralBlatt

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§17.12.

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Bailey’s Transform, Lemma, Chains and Tree. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.

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ISBN 0-7923-7119-4, MathReview, ZentralBlatt

Referenced by:

§17.12.

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12: 4.48 Software

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Bailey (1993). Fortran.

… ►See also Bailey (1995), Hull and Abrham (1986), Xu and Li (1994). …

13: 17.4 Basic Hypergeometric Functions

… ►It is slightly at variance with the notation in Bailey (1964) and Slater (1966). In these references the factor ${\left({(-1)}^n{q}^{\left(\genfrac{}{}{0.0pt}{}{n}{2}\right)}\right)}^{s-r}$ is not included in the sum. … ►Here and elsewhere the $b_j$ must not take any of the values $q^{-n}$, and the $a_j$ must not take any of the values $q^{n+1}$. The infinite series converge when $s\ge r$ provided that and also, in the case $s=r$, . … ►The following definitions apply when and : …

14: 17.9 Further Transformations of ${}_{r+1}{}^{}\varphi _r^{}$ Functions

§17.9 Further Transformations of ${}_{r+1}{}^{}\varphi _r^{}$ Functions

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Sears’ Balanced ${}_4{}^{}\varphi _3^{}$ Transformations

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Bailey’s Transformation of Very-Well-Poised ${}_8{}^{}\varphi _7^{}$

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§17.9(iv) Bibasic Series

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15: Bibliography W

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A note on the trinomial analogue of Bailey’s lemma. J. Combin. Theory Ser. A 81 (1), pp. 114–118.

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ISSN 0097-3165, Document, MathReview (Anne Schilling), ZentralBlatt

Referenced by:

§17.12.

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The Airy transform. Amer. Math. Monthly 86 (4), pp. 271–277.

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ISSN 0002-9890, FullText, Document, MathReview (A. G. Ramm), ZentralBlatt

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(9.10.13), §9.10(ix), §9.10(v).

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Asymptotics for the ${}_4{}^{}F_3^{}$ polynomials. J. Approx. Theory 66 (1), pp. 58–71.

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ISSN 0021-9045, Document, MathReview (R. G. Buschman), ZentralBlatt

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§18.26(v).

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Elliptic genera and quantum field theory. Comm. Math. Phys. 109 (4), pp. 525–536.

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ISSN 0010-3616, Document, MathReview (J. Stasheff), ZentralBlatt

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1st item.

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Algorithm 44: Bessel functions computed recursively. Comm. ACM 4 (4), pp. 177–178.

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Notes:

Includes Algol code, maximum accuracy 8S.

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ISSN 0001-0782, Document

Referenced by:

§10.77(ii).

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16: 5.24 Software

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Bailey (1993). Fortran and C++ wrapper.

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17: Bibliography M

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On the computation of zeroes of $J_n(z)-i{J}_{n+1}(z)=0$ . Quart. Appl. Math. 55 (4), pp. 623–633.

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ISSN 0033-569X, MathReview (Andrea Laforgia), ZentralBlatt

Referenced by:

§10.21(ix).

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Associated Wilson polynomials. Constr. Approx. 7 (4), pp. 521–534.

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ISSN 0176-4276, Document, MathReview (R. A. Askey), ZentralBlatt

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§16.4(iii).

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Evaluation of complex logarithms and related functions. SIAM J. Numer. Anal. 18 (4), pp. 744–750.

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ISSN 0036-1429, Document, MathReview (M. Brannigan), ZentralBlatt

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§4.45(ii).

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A $q$-analog of the ${}_5{}^{}F_4^{}(1)$ summation theorem for hypergeometric series well-poised in $\mathrm{𝑆𝑈}(n)$ . Adv. in Math. 57 (1), pp. 14–33.

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ISSN 0001-8708, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§17.15.

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The $A_l$ and $C_l$ Bailey transform and lemma. Bull. Amer. Math. Soc. (N.S.) 26 (2), pp. 258–263.

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ISSN 0273-0979, Pdf, Document, MathReview (Robert A. Gustafson), ZentralBlatt

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§17.12.

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18: Bibliography S

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Zur Berechnung der Eigenwerte der Sphäroiddifferentialgleichung. Numer. Math. 4, pp. 310–312 (German).

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ISSN 0029-599X, Document, MathReview (I. Marx), ZentralBlatt

Referenced by:

§30.16(i).

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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations. SIAM J. Math. Anal. 10 (4), pp. 823–838.

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ISSN 0036-1410, Document, MathReview (Ernest G. Kalnins), ZentralBlatt

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§28.32(i).

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On parabolic cylinder functions. J. Inst. Math. Appl. 4 (1), pp. 106–112.

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Document, MathReview (F. M. Arscott), ZentralBlatt

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§12.16.

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Multiplicative processes and power laws. Phys. Rev. E 57 (4), pp. 4811–4813.

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Document

Referenced by:

§8.24(i).

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An elliptic incarnation of the Bailey chain. Int. Math. Res. Not. 2002 (37), pp. 1945–1977.

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ISSN 1073-7928, Document, MathReview (S. Ole Warnaar), ZentralBlatt

Referenced by:

§17.12.

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19: 17.6 ${}_2{}^{}\varphi _1^{}$ Function

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$q$-Gauss Sum

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First $q$-Chu–Vandermonde Sum

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Second $q$-Chu–Vandermonde Sum

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Andrews–Askey Sum

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Bailey–Daum $q$-Kummer Sum

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20: 18.18 Sums

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§18.18(vi) Bateman-Type Sums

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Jacobi

… ►For the Poisson kernel of Jacobi polynomials (the Bailey formula) see Bailey (1938). ►

§18.18(viii) Other Sums

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