Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Trigonometric Functions of Real Numbers01:30

Trigonometric Functions of Real Numbers

The unit circle—a circle with a radius of one, centered at the origin of the coordinate plane—serves as the foundational framework for defining trigonometric functions. In this context, arc length refers to the distance measured along the circumference of the circle between two points, and it provides a way to represent real numbers geometrically. Each real number t corresponds to an arc length measured counterclockwise from the positive x-axis around the circle. The coordinates of a point on...
Rationalizing Substitutions01:29

Rationalizing Substitutions

Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...
Binomial Expansion Using Pascal's Triangle01:30

Binomial Expansion Using Pascal's Triangle

Expanding a binomial expression such as (a + b)n results in a predictable sequence of terms that can be systematically derived using Pascal’s Triangle. This triangular array of numbers plays a central role in understanding and computing the coefficients of binomial expansions.Pascal’s Triangle is constructed such that each row corresponds to the coefficients of a binomial raised to a power. The topmost row, known as the zeroth row, corresponds to (a + b)0, and each successive row gives the...
Trigonometric Identities I01:27

Trigonometric Identities I

Trigonometric identities are equations that relate trigonometric functions and hold for all angles within their domains. A fundamental identity among these is the Pythagorean identity, which arises directly from the geometry of the unit circle. For any angle θ, a point on the unit circle has coordinates (cos⁡ θ, sin ⁡θ), and since the radius of the circle is one, the Pythagorean Theorem gives:This identity serves as the basis for deriving additional identities. Dividing the Pythagorean identity...
Trigonometric Substitution01:23

Trigonometric Substitution

Trigonometric substitution is a technique used to simplify integrals that contain square root expressions involving quadratic forms. It is particularly effective when the integrand includes terms resembling those found in standard geometric equations, such as circles or ellipses.Molniya satellites follow highly elliptical orbits, repeatedly sweeping out the same regions of space as they revolve around Earth. To estimate the area enclosed by such an orbit, the path is modeled as an ellipse...
Derivatives of the Trigonometric Functions01:26

Derivatives of the Trigonometric Functions

The motion of a Ferris wheel rotating at a constant speed provides an intuitive model for understanding trigonometric functions and their derivatives. As a rider moves along the circular path, the vertical height above the ground changes smoothly and periodically over time. This vertical motion can be accurately represented by a sine function, reflecting the repeating pattern of ascent and descent inherent to circular motion.Height and Rate of ChangeIf the rider’s height is modeled by a sine...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Perioperative Management: HeartMate 3 Left Ventricular Assist Devices in Non-Cardiac Surgery.

Journal of cardiothoracic and vascular anesthesia·2026
Same author

Optimisation of direct-acting oral anticoagulants (DOACs) use for atrial fibrillation (AF) and venous thromboembolism: a practical guide.

Expert opinion on pharmacotherapy·2026
Same author

Hospitalizations during the 30-day period preceding admission with pulmonary embolism: insights from the National Readmission Database.

Hospital practice (1995)·2025
Same author

The dimensionality of recognition memory: A state-trace analysis of the effects of dividing attention.

Journal of experimental psychology. Learning, memory, and cognition·2025
Same author

Ramanujan's partition generating functions modulo <math><mi>ℓ</mi></math>.

The Ramanujan journal·2025
Same author

Symmetric and asymmetric ligands for Fe<sup>III</sup> spin crossover - the influence of the <i>C</i><sub>2</sub> axis.

Dalton transactions (Cambridge, England : 2003)·2025
Same journal

Tau protein as a regulator of mitochondrial function and dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

A scalable, dividing cell model for the robust propagation and quantification of human sporadic Creutzfeldt-Jakob disease prions.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Epigenetic regulation of mesenchymal BMP signaling directs postnatal organ innervation.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Single-shot wide-field biochemical imaging at 1 kHz frame rate.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Morphogenesis and topological evolution of a frustrated nematic liquid crystal under confinement.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

B cell-intrinsic CXCR3 drives efficient generation of ectopic pulmonary germinal center responses to influenza A virus infection.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

Related Experiment Video

Updated: May 12, 2026

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

Ramanujan's mock theta functions.

Michael Griffin1, Ken Ono, Larry Rolen

  • 1Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA. mjgrif3@emory.edu

Proceedings of the National Academy of Sciences of the United States of America
|March 29, 2013
PubMed
Summary
This summary is machine-generated.

This study confirms that Ramanujan

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Related Experiment Videos

Last Updated: May 12, 2026

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
12:34

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Number Theory
  • Mathematical Physics

Background:

  • Srinivasa Ramanujan introduced mock theta functions in his deathbed letter.
  • Zwegers' work connected these functions to harmonic weak Maass forms.
  • Ramanujan's original definition has received limited attention.

Purpose of the Study:

  • To verify Ramanujan's original definition of mock theta functions.
  • To bridge the gap between Ramanujan's initial concept and modern interpretations.

Main Methods:

  • Analysis of Ramanujan's original manuscripts and definitions.
  • Comparison of Ramanujan's examples with established theories of mock theta functions.

Main Results:

  • Ramanujan's purported examples of mock theta functions satisfy his original definition.
  • The study validates the historical accuracy of Ramanujan's work.

Conclusions:

  • Ramanujan's initial definition of mock theta functions is consistent with his examples.
  • This research provides a foundational link for understanding mock theta functions.