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Fractional calculus
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111	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
112	15 Higher and Super Calculus of Elliptic Integral 15.1 Double series expansion of Elliptic Integral[removed]Double series expansion of Elliptic Integral of the 1st kind Formula[removed]The following expressions hold for \|k Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-11 01:10:58 Polar coordinate system Integral calculus Elliptic integral Binomial coefficient Binomial theorem Tautochrone curve Vibrations of a circular drum Mathematics Mathematical analysis Curves
113	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
114	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
115	16 Higher Integral of the Product of Two Functions 16.1 Higher Integral of f (x) g (x[removed]Higher Intagration by parts Formula[removed]Let of Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-12 02:58:20 Differential calculus Integral calculus Integration by parts Differential equation Integral Derivative Differentiation rules Mathematical analysis Mathematics Functions and mappings
116	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
117	6 Superellipse (Lamé curve) 6.1 Equations of a superellipse A superellipse (horizontally long) is expressed as follows. Implicit Equation n Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-10 10:09:18 Curves Integral calculus Orthogonal polynomials Superellipse Polynomials Arc length Ellipse Differential equation Binomial theorem Mathematical analysis Mathematics Geometry
118	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
119	14 Higher and Super Calculus of Logarithmic Integral etc[removed]Higher Integral of Exponential Integral Exponential Integral is defined as follows. x t Ei(x) = Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-11 01:11:01 Integral calculus Special functions Integrals Logarithms Trigonometric integral Trigonometry Antiderivative Exponential integral Integration by parts Calculus Mathematical analysis Mathematics
120	20 Higher Calculus of the product of many functions 20.1 Higher Derivative of the product of many functions (1) Binomial Theorem and Leibniz Rule According to the binomial theorem in 3.1 , the following expression holds Add to Reading List Source URL: fractional-calculus.com Language: English - Date: 2013-11-11 05:31:46 Integral calculus Functions and mappings Leibniz integral rule Multivariable calculus Derivative Sigma-algebra Normal distribution Mathematical analysis Calculus Mathematics

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