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

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(5/2), -(5/2)}, z] == (1/3189375) (3189375 + 16839900 z + 170270100 z^2 + 13621608000 z^3 + 830334304800 z^4 + 4847476233600 z^5 + 9223316968320 z^6 + 8103665710080 z^7 + 3870381024000 z^8 + 1099400924160 z^9 + 195603448320 z^10 + 22400504832 z^11 + 1663752048 z^12 + 79100160 z^13 + 2307328 z^14 + 37376 z^15 + 256 z^16) + (1/3189375) (8 E^z Sqrt[Pi] (13232419200 z^(7/2) + 238183545600 z^(9/2) + 955140076800 z^(11/2) + 1518304435200 z^(13/2) + 1207304028000 z^(15/2) + 543008370240 z^(17/2) + 148470325920 z^(19/2) + 25757602560 z^(21/2) + 2899443465 z^(23/2) + 212774250 z^(25/2) + 10029432 z^(27/2) + 290736 z^(29/2) + 4688 z^(31/2) + 32 z^(33/2)) 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]