Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aflz)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1, a₂>=1

For fixed z and a₁=1, a₂=11/2, b₁>=-11/2

For fixed z and a₁=1, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.aflz.01

Input Form

HypergeometricPFQ[{1, 11/2}, {-(11/2), -(7/2)}, -z] == (1/1031443875) (1031443875 - 294698250 z + 170270100 z^2 - 243243000 z^3 + 1654052400 z^4 + 20951330400 z^5 + 293318625600 z^6 - 1390537653120 z^7 + 1629097747200 z^8 - 821322754560 z^9 + 214369735680 z^10 - 31428802560 z^11 + 2662477824 z^12 - 128163840 z^13 + 3227648 z^14 - 32768 z^15) + (1/1031443875) ((32768 Sqrt[Pi] (-19958400 z^(13/2) + 59875200 z^(15/2) - 59875200 z^(17/2) + 27941760 z^(19/2) - 6985440 z^(21/2) + 997920 z^(23/2) - 83160 z^(25/2) + 3960 z^(27/2) - 99 z^(29/2) + z^(31/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]