Rational Poly-Exponential Functions - Euler numbers

Definition.

All of the odd Euler numbers are 0. Hence, the only multisectioning of interest, is by an even amount.

Either the recurrences can be used as given below with the formula above, or code written for this purpose can be used to perform these calculations.

Some Recurrences

• Multisectioning by 2.
  • Bottom Recurrence
  • Top recurrence at 0
• Multisectioning by 4.
  • Bottom Recurrence
  • Top recurrence at 0
  • Top recurrence at 2
• Multisectioning by 6.
  • Bottom Recurrence
  • Top recurrence at 0
  • Top recurrence at 2
  • Top recurrence at 4
• Multisectioning by 8.
  • Bottom Recurrence
  • Top recurrence at 0
  • Top recurrence at 2
  • Top recurrence at 4
  • Top recurrence at 6
• Multisectioning by 10.
  • Bottom Recurrence
  • Top recurrence at 0
  • Top recurrence at 2
  • Top recurrence at 4
  • Top recurrence at 6
  • Top recurrence at 8
• Multisectioning by 12.
  • Bottom Recurrence
  • Top recurrence at 0
  • Top recurrence at 2
  • Top recurrence at 4
  • Top recurrence at 6
  • Top recurrence at 8
  • Top recurrence at 10
• Multisectioning by 14.
  • Bottom Recurrence
  • Top recurrence at 0
  • Top recurrence at 2
  • Top recurrence at 4
  • Top recurrence at 6
  • Top recurrence at 8
  • Top recurrence at 10
  • Top recurrence at 12
• Multisectioning by 16.
  • Bottom Recurrence
  • Top recurrence at 0
  • Top recurrence at 2
  • Top recurrence at 4
  • Top recurrence at 6
  • Top recurrence at 8
  • Top recurrence at 10
  • Top recurrence at 12
  • Top recurrence at 14
  • Bottom Recurrence (low memory requirements)
  • Top recurrence at 0 (low memory requirements)
• Multisectioning by 18.
  • Bottom Recurrence
• Multisectioning by 20.
  • Bottom Recurrence
• Multisectioning by 24.
  • Bottom Recurrence

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This file was last modified April 14, 1999 .