Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an0q)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.an0q.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(11/2), -(11/2)}, z] == (1/170188239375) (170188239375 + 151903552500 z + 144402142500 z^2 + 204324120000 z^3 + 551675124000 z^4 + 4168212048000 z^5 + 290385439344000 z^6 + 16559908106112000 z^7 + 95389309247904000 z^8 + 186584428079078400 z^9 + 174461072462208000 z^10 + 91601955938304000 z^11 + 29574586873036800 z^12 + 6205201319116800 z^13 + 875290744258560 z^14 + 84586463216640 z^15 + 5635194808320 z^16 + 257075735040 z^17 + 7846062080 z^18 + 152408064 z^19 + 1695744 z^20 + 8192 z^21) + (1/170188239375) (256 E^z Sqrt[Pi] (8491881888000 z^(13/2) + 147192619392000 z^(15/2) + 590352298704000 z^(17/2) + 970046334432000 z^(19/2) + 822296499192000 z^(21/2) + 406589592729600 z^(23/2) + 126265641415200 z^(25/2) + 25806888878400 z^(27/2) + 3574431985950 z^(29/2) + 340955710200 z^(31/2) + 22499970675 z^(33/2) + 1019236890 z^(35/2) + 30943080 z^(37/2) + 598640 z^(39/2) + 6640 z^(41/2) + 32 z^(43/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> Erf </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]