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

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=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(9/2), -(5/2)}, z] == (1/4465125) (4465125 + 8930250 z + 28066500 z^2 + 340540200 z^3 - 6810804000 z^4 + 138940401600 z^5 + 1028519856000 z^6 + 1836684460800 z^7 + 1417540642560 z^8 + 577727193600 z^9 + 137143319040 z^10 + 19955335680 z^11 + 1818277440 z^12 + 103292736 z^13 + 3527040 z^14 + 65792 z^15 + 512 z^16) + (1/4465125) (32 E^z Sqrt[Pi] (11427998400 z^(11/2) + 50107377600 z^(13/2) + 73915707600 z^(15/2) + 51757801200 z^(17/2) + 19943317800 z^(19/2) + 4572688680 z^(21/2) + 650529495 z^(23/2) + 58382505 z^(25/2) + 3282000 z^(27/2) + 111240 z^(29/2) + 2064 z^(31/2) + 16 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]