The Helpful Mathematics
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Article 11

Function handbook

Category. Mathematics.

Abstract. Function handbook contains all elementary, trigonometric and hyperbolic functions — their definitions, graphs, properties and identities.

References. The handbook is a part of scientific calculator Li-L and scientific calculator Li-X products.

Function handbook

1. Introduction

When working at scientific calculator Li-L project we wanted to give some gift to its the future users. This scientific calculator has an embedded Help available just in two clicks for every part of the application and we had an idea to create function handbook and include it as a part of the Help, so that click in the Li-L calculator keypad took the user to the handbook page with function description.

The most challenging part of the idea was graphics. We wanted every function to have its graph and we set high standards for graphics: it was to be properly scaled, numbered and antialiased. It was interesting and difficult job: every figure was created in several stages with final stage of editing on pixel level. When the task was completed, maybe first time in my life I saw all the functions in the same scale, properly curved and cut, so that all the features were clearly visible.

The result got was so great we decided to put this beauty online. And now you can access what Li-L calculator users have on their desktops. Below you will find functions put into several lists — every list holds all functions, but ordering is different, so that you can look up the function by its notation, name or article head.

Li-L calculator handbook contains all elementary, trigonometric and hyperbolic functions. Scientific calculator Li-X got handbook extended with gamma and Bessel functions and scientific calculator Li-Xc got handbook extended with modified Bessel functions.

2. Content

  1. or sqrt — square root
  2. ^ — power
  3. Γ — gamma function
  4. abs — absolute value
  5. arccos — trigonometric arc cosine
  6. arccot or arcctg — trigonometric arc cotangent
  7. arccsc or arccosec — trigonometric arc cosecant
  8. arcosh or arch — arc-hyperbolic cosine
  9. arcoth or arcth — arc-hyperbolic cotangent
  10. arcsch — arc-hyperbolic cosecant
  11. arcsec — trigonometric arc secant
  12. arcsin — trigonometric arc sine
  13. arctan or arctg — trigonometric arc tangent
  14. arsech or arsch — arc-hyperbolic secant
  15. arsinh or arsh — arc-hyperbolic sine
  16. artanh or arth — arc-hyperbolic tangent
  17. ceil — ceiling
  18. cos — trigonometric cosine
  19. cosh or ch — hyperbolic cosine
  20. cot or ctg — trigonometric cotangent
  21. coth or cth — hyperbolic cotangent
  22. csc or cosec — trigonometric cosecant
  23. csch — hyperbolic cosecant
  24. exp — exponent
  25. floor — floor
  26. Iν — modified Bessel function of the first kind
  27. Jν — Bessel function of the first kind
  28. Kν — modified Bessel function of the second kind
  29. ln — natural logarithm
  30. log or lg — decimal logarithm
  31. n! — factorial
  32. sec — trigonometric secant
  33. sech — hyperbolic secant
  34. sign — signum
  35. sin — trigonometric sine
  36. sinh or sh — hyperbolic sine
  37. tan or tg — trigonometric tangent
  38. tanh or th — hyperbolic tangent
  39. Yν — Bessel function of the second kind

3. Function index by name

  1. Absolute value abs
  2. Arc-hyperbolic cosecant arcsch
  3. Arc-hyperbolic cosine arcosh or arch
  4. Arc-hyperbolic cotangent arcoth or arcth
  5. Arc-hyperbolic secant arsech or arsch
  6. Arc-hyperbolic sine arsinh or arsh
  7. Arc-hyperbolic tangent artanh or arth
  8. Bessel function of the first kind Jν
  9. Bessel function of the second kind Yν
  10. Ceiling function ceil
  11. Decimal logarithm log or lg
  12. Exponent exp
  13. Factorial n!
  14. Floor function floor
  15. Gamma function Γ
  16. Hyperbolic cosecant csch
  17. Hyperbolic cosine cosh or ch
  18. Hyperbolic cotangent coth or cth
  19. Hyperbolic secant sech
  20. Hyperbolic sine sinh or sh
  21. Hyperbolic tangent tanh or th
  22. Modified Bessel function of the first kind Iν
  23. Modified Bessel function of the second kind Kν
  24. Natural logarithm ln
  25. Power ^
  26. Signum sign
  27. Square root or sqrt
  28. Trigonometric arc cosecant arccsc or arccosec
  29. Trigonometric arc cosine arccos
  30. Trigonometric arc cotangent arccot or arcctg
  31. Trigonometric arc secant arcsec
  32. Trigonometric arc sine arcsin
  33. Trigonometric arc tangent arctan or arctg
  34. Trigonometric cosecant csc or cosec
  35. Trigonometric cosine cos
  36. Trigonometric cotangent cot or ctg
  37. Trigonometric secant sec
  38. Trigonometric sine sin
  39. Trigonometric tangent tan or tg

4. Function index by notation

  1. — square root
  2. ^ — power
  3. Γ — gamma function
  4. abs — absolute value
  5. arccos — trigonometric arc cosine
  6. arccosec — trigonometric arc cosecant
  7. arccot — trigonometric arc cotangent
  8. arccsc — trigonometric arc cosecant
  9. arcctg — trigonometric arc cotangent
  10. arch — arc-hyperbolic cosine
  11. arcosh — arc-hyperbolic cosine
  12. arcoth — arc-hyperbolic cotangent
  13. arcsch — arc-hyperbolic cosecant
  14. arcsec — trigonometric arc secant
  15. arcsin — trigonometric arc sine
  16. arctan — trigonometric arc tangent
  17. arctg — trigonometric arc tangent
  18. arcth — arc-hyperbolic cotangent
  19. arsch — arc-hyperbolic secant
  20. arsech — arc-hyperbolic secant
  21. arsh — arc-hyperbolic sine
  22. arsinh — arc-hyperbolic sine
  23. artanh — arc-hyperbolic tangent
  24. arth — arc-hyperbolic tangent
  25. ceil — ceiling
  26. ch — hyperbolic cosine
  27. cos — trigonometric cosine
  28. cosec — trigonometric cosecant
  29. cosh — hyperbolic cosine
  30. cot — trigonometric cotangent
  31. coth — hyperbolic cotangent
  32. csc — trigonometric cosecant
  33. csch — hyperbolic cosecant
  34. ctg — trigonometric cotangent
  35. exp — exponent
  36. floor — floor
  37. Iν — modified Bessel function of the first kind
  38. Jν — Bessel function of the first kind
  39. Kν — modified Bessel function of the second kind
  40. lg — decimal logarithm
  41. ln — natural logarithm
  42. log — decimal logarithm
  43. n! — factorial
  44. sec — trigonometric secant
  45. sech — hyperbolic secant
  46. sh — hyperbolic sine
  47. sign — signum
  48. sin — trigonometric sine
  49. sinh — hyperbolic sine
  50. sqrt — square root
  51. tan — trigonometric tangent
  52. tanh — hyperbolic tangent
  53. tg — trigonometric tangent
  54. th — hyperbolic tangent
  55. Yν — Bessel function of the second kind

 

Write to the author of the article — Sergey Chernenko.