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Bernoulli number
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101	3 Formulas for Riemann Zeta at odd number Formulas for Zeta at odd number obtained in " 1 Zeta Generating Functions " were automorphisms which were expressed by the lower zetas. In this chapter, removing the lower zetas, Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-12 03:41:00 Number theory Mathematical series Trigonometry Real analysis Taylor series Euler number Trigonometric functions Bernoulli number Riemann zeta function Mathematical analysis Mathematics Integer sequences
102	Probability Reference Combinatorics and Sampling A permutation is an ordered selection. The number of permutations of k items picked from a list of n items, without replacement, is P (n; k) := n(n \| Add to Reading List Source URL: uhaweb.hartford.edu Language: English - Date: 2014-02-20 15:32:39 Polynomials Beta function Negative binomial distribution Probability density function Orthogonal polynomials Mathematical series Bernoulli polynomials Binomial coefficient Mathematical analysis Mathematics Special functions
103	05 Termwise Higher Integral (Trigonometric, Hyperbolic) In this chapter, for the function which second or more order integral cannot be expressed with the elementary functions among trigonometric functions and hyperbolic Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-10 10:41:22 Number theory Trigonometry Complex analysis Mathematical series Hyperbolic function 2K Trigonometric functions Fourier series Bernoulli number Mathematical analysis Mathematics Analytic functions
104	4 Euler-Maclaurin Summation Formula 4.1 Bernoulli Number & Bernoulli Polynomial[removed]Definition of Bernoulli Number Bernoulli numbers Bk (k =1, 2, 3, ) are defined as coefficients of the following equation. Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-10 10:09:05 Integer sequences Summability methods Bernoulli polynomials Polynomials Bernoulli number Euler–Maclaurin formula Binomial coefficient Summation Euler summation Mathematics Mathematical analysis Number theory
105	2 Formulas for Riemann Zeta at natural number Formulas for Zeta at natural number obtained in " 1 Zeta Generating Functions " were automorphisms which were expressed by the lower zetas. In this chapter, removing the lowe Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-12 03:40:56 Number theory Bernoulli number Topology
106	5 Formulas for Riemann Zeta at complex number We can extend "2 Formulas for Riemann Zeta at natural number " to the complex number easily. 5.1 Formulas of coth x family Formula[removed]When Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-11 09:40:27 Complex analysis Number theory Bernoulli number Topology Riemann zeta function Gamma function Ramanujan summation Mathematical analysis Mathematics Meromorphic functions
107	´ COMPUTING THE EULER-POINCARE CHARACTERISTICS OF SIGN CONDITIONS Saugata Basu, Richard Pollack, and Marie-Franc Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:52 Algebraic topology Topological graph theory Algebraic geometry Euler characteristic Betti number Algebraic variety Field extension Simplicial complex Bernoulli number Abstract algebra Mathematics Topology
108	10 Termwise Higher Derivative (Trigonometric, Hyperbolic) In this chapter, for the function which the second or more order derivative is difficult to express with an easy unification notation among trigonometric function Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-10 20:30:43 Trigonometry Integer sequences Analytic functions Complex analysis Trigonometric functions Hyperbolic function 2K Taylor series Bernoulli number Mathematical analysis Mathematics Number theory
109	13 Termwise Super Derivative In this chapter, for the function whose super derivatives are difficult to be expressed with easy formulas, we differentiate the series expansion of these functions non integer times termwise Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-12 02:58:29 Integer sequences Bernoulli number Factorial Hyperbolic function 2K Bernoulli polynomials Ramanujan summation Mathematics Mathematical analysis Number theory
110	08 Termwise Super Integral In this chapter, for the function which super (non-integer order) integral cannot be expressed with elementary functions, we integrate with the series expansion of these function non-integer ti Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-10 10:41:29 Integer sequences Mathematical series Inverse trigonometric functions Trigonometry Integral Bernoulli number Pi Factorial Ramanujan summation Mathematics Mathematical analysis Number theory

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