MOSCOW MATHEMATICAL JOURNAL Volume 9, Number 1, January–March 2009, Pages 57–89 FROM CLAUSEN TO CARLITZ: LOW-DIMENSIONAL SPIN GROUPS AND IDENTITIES AMONG CHARACTER SUMS NICHOLAS M. KATZ

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Learning to Discover Efficient Mathematical Identities by Wojciech Zaremba, Karol Kurach, and Rob Fergus ref: http://arxiv.org/abs

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A Non-Holonomic Systems Approach to Special Function Identities

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• Mathematical analysis
• Mathematics
• Special functions
• Holonomic function
• Holonomic constraints
• Recurrence relation
• Differential forms on a Riemann surface
• Transcendental number

Name:_______________________ Date assigned:______________ Band:________ Precalculus | Packer Collegiate Institute Trig Identities Section 0: Warm Up Identities are things that on the surface look different

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• Mathematics
• Trigonometry
• Mathematical analysis
• English-language films
• Trigonometric functions
• Super
• Cross-multiplication
• Identity
• Film

1 ¨ 1 = f (|q|)q/|q| and m2 q ¨ 2 = −f (|q|)q/|q|. MultiplyI immediately have m1 q ing these equations by m2 and m1 (respectively) and then subtracting, I get ¨ 2 ) = (m2 + m1 )f (|q|)q/|q|. The desired equation fol

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• Trigonometry
• Mathematical identities
• Bearing pressure
• Bearings
• Mechanical engineering

ES 111 Mathematical Methods in the Earth Sciences Lecture Outline 1 - Sept 24th ’15 Review of trigonometry and basic calculus Trigonometry When is it useful? Everywhere! Anything involving coordinate systems (e.g. maps

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• Mathematical analysis
• Mathematics
• Calculus
• Differentiation rules
• Integral calculus
• Differential calculus
• Trigonometry
• Mathematical identities
• Product rule
• Chain rule
• Sine
• Derivative

FROM CLAUSEN TO CARLITZ: LOW-DIMENSIONAL SPIN GROUPS AND IDENTITIES AMONG CHARACTER SUMS NICHOLAS M. KATZ Dedicated to Pierre Deligne, with the utmost admiration

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• Mathematics
• Mathematical analysis
• Algebra
• Ordinary differential equations
• Algebraic topology
• Sheaf
• Kloosterman sum
• Hypergeometric function
• Cohomology
• Lie groups
• Linear temporal logic
• Differential forms on a Riemann surface

BEST APPROXIMATIONS IN L1 ARE NEAR BEST IN Lp , p < 1 LAWRENCE G. BROWN AND BRADLEY J. LUCIER (Communicated by J. Marshall Ash) Abstract. We show that any best L1 polynomial approximation to a function f in Lp , 0 < p <

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• Differentiation rules
• Functions and mappings
• Ordinary differential equations
• Mathematical identities
• Integral calculus
• Product rule
• SturmLiouville theory

q-SERIES IDENTITIES AND VALUES OF CERTAIN L-FUNCTIONS ´nez-Urroz and Ken Ono George E. Andrews, Jorge Jime Appearing in the Duke Mathematical Journal.

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Learning to Discover Efficient Mathematical Identities Wojciech Zaremba1 Karol Kurach2 and Rob Fergus1,3 1

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