Mehler–Dirichlet formula
(0.001 seconds)
21—30 of 257 matching pages
21: 25.1 Special Notation
…
►The main related functions are the Hurwitz zeta function , the dilogarithm , the polylogarithm (also known as Jonquière’s function ), Lerch’s transcendent , and the Dirichlet
-functions .
22: Bibliography
…
►
Dirichlet series related to the Riemann zeta function.
J. Number Theory 19 (1), pp. 85–102.
…
►
Formulas for higher derivatives of the Riemann zeta function.
Math. Comp. 44 (169), pp. 223–232.
►
Note on the trivial zeros of Dirichlet
-functions.
Proc. Amer. Math. Soc. 94 (1), pp. 29–30.
►
Modular Functions and Dirichlet Series in Number Theory.
2nd edition, Graduate Texts in Mathematics, Vol. 41, Springer-Verlag, New York.
…
►
Bernoulli’s power-sum formulas revisited.
Math. Gaz. 90 (518), pp. 276–279.
…
23: 27.4 Euler Products and Dirichlet Series
§27.4 Euler Products and Dirichlet Series
… ►
27.4.4
►called Dirichlet series with coefficients .
The function is a generating function, or more precisely, a Dirichlet generating
function, for the coefficients.
…
24: 25.11 Hurwitz Zeta Function
…
►
§25.11(iii) Representations by the Euler–Maclaurin Formula
►
25.11.5
, , , .
►
25.11.6
, , .
►
25.11.7
, , , .
…
►
…
25: 27.20 Methods of Computation: Other Number-Theoretic Functions
…
►The recursion formulas (27.14.6) and (27.14.7) can be used to calculate the partition function for .
…
►A recursion formula obtained by differentiating (27.14.18) can be used to calculate Ramanujan’s function , and the values can be checked by the congruence (27.14.20).
…
26: 25.21 Software
…
►
§25.21(ix) Dirichlet -series
…27: Bibliography M
…
►
Siegel’s modular forms and Dirichlet series.
Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin.
…
►
A determinant formula for a class of rational solutions of Painlevé V equation.
Nagoya Math. J. 168, pp. 1–25.
►
On a class of algebraic solutions to the Painlevé VI equation, its determinant formula and coalescence cascade.
Funkcial. Ekvac. 46 (1), pp. 121–171.
…
►
Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions.
Ramanujan J. 6 (1), pp. 7–149.
…
►
The -analogue of Stirling’s formula.
Rocky Mountain J. Math. 14 (2), pp. 403–413.
…
28: 27.9 Quadratic Characters
§27.9 Quadratic Characters
… ►The Legendre symbol , as a function of , is a Dirichlet character (mod ). … ►The Jacobi symbol is a Dirichlet character (mod ). …29: Howard S. Cohl
…
►Howard is the project leader for the NIST Digital Repository of Mathematical Formulae seeding and development projects.
In this regard, he has been exploring mathematical knowledge management and the digital expression of mostly unambiguous context-free full semantic information for mathematical formulae.
30: Preface
…
►Abramowitz and Stegun’s Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables is being completely rewritten with regard to the needs of today.
…The authors will review the relevant published literature and produce approximately twice the number of formulas that were contained in the original Handbook.
…