fractional or multiple
(0.001 seconds)
31—40 of 178 matching pages
31: 17.4 Basic Hypergeometric Functions
32: 10.10 Continued Fractions
§10.10 Continued Fractions
…33: 10.33 Continued Fractions
§10.33 Continued Fractions
…34: 2.6 Distributional Methods
…
►However, they are multiples of the derivatives of .
…
►
§2.6(iii) Fractional Integrals
►The Riemann–Liouville fractional integral of order is defined by … ►If both and in (2.6.34) have asymptotic expansions of the form (2.6.9), then the distribution method can also be used to derive an asymptotic expansion of the convolution ; see Li and Wong (1994). … ►Multiplication of these expansions leads to …35: Bibliography O
…
►
Connection formulas for second-order differential equations with multiple turning points.
SIAM J. Math. Anal. 8 (1), pp. 127–154.
►
Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities.
SIAM J. Math. Anal. 8 (4), pp. 673–700.
►
Second-order differential equations with fractional transition points.
Trans. Amer. Math. Soc. 226, pp. 227–241.
…
36: 4.21 Identities
…
►
§4.21(iii) Multiples of the Argument
… ►This result is also valid when is fractional or complex, provided that . …37: 31.11 Expansions in Series of Hypergeometric Functions
…
►In this case the accessory parameter is a root of the continued-fraction equation
…
►The expansion (31.11.1) for a Heun function that is associated with any branch of (31.11.2)—other than a multiple of the right-hand side of (31.11.12)—is convergent inside the ellipse .
…
►
§31.11(v) Doubly-Infinite Series
►Schmidt (1979) gives expansions of path-multiplicative solutions (§31.6) in terms of doubly-infinite series of hypergeometric functions. …38: 31.6 Path-Multiplicative Solutions
§31.6 Path-Multiplicative Solutions
►A further extension of the notation (31.4.1) and (31.4.3) is given by …These solutions are called path-multiplicative. …39: Wadim Zudilin
…
►Zudilin is author or coauthor of numerous publications including the book Neverending Fractions, An Introduction to Continued Fractions published by Cambridge University Press in 2014.
…
40: Bibliography S
…
►
Algorithm 786: Multiple-precision complex arithmetic and functions.
ACM Trans. Math. Software 24 (4), pp. 359–367.
…
►
Efficient multiple-precision evaluation of elementary functions.
Math. Comp. 52 (185), pp. 131–134.
►
Algorithm 693: A FORTRAN package for floating-point multiple-precision arithmetic.
ACM Trans. Math. Software 17 (2), pp. 273–283.
…
►
Multiplicative processes and power laws.
Phys. Rev. E 57 (4), pp. 4811–4813.
…
►
Approximate Calculation of Multiple Integrals.
Prentice-Hall Inc., Englewood Cliffs, N.J..
…