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

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=5, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5, 6}, {-(9/2), 1}, z] == (1/21772800) (21772800 - 145152000 z + 435456000 z^2 - 1083801600 z^3 + 3251404800 z^4 - 23410114560 z^5 - 59752496475 z^6 - 46600070400 z^7 - 17303797080 z^8 - 3541793760 z^9 - 425148864 z^10 - 30432000 z^11 - 1267840 z^12 - 28160 z^13 - 256 z^14) + (1/43545600) (E^z Sqrt[Pi] (-83309314725 z^(11/2) - 154787720850 z^(13/2) - 107792722800 z^(15/2) - 37789768800 z^(17/2) - 7481224800 z^(19/2) - 879529920 z^(21/2) - 62104320 z^(23/2) - 2563584 z^(25/2) - 56576 z^(27/2) - 512 z^(29/2)) Erf[Sqrt[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]