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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(11/2), 3}, z] == (1/9282994875) (4 E^(z/2) (2434768875 - 5285857500 z + 6641384400 z^2 - 7201353600 z^3 + 8423805600 z^4 - 13533609600 z^5 + 55373673600 z^6 + 190469283840 z^7 + 150368106240 z^8 + 52060124160 z^9 + 9383700480 z^10 + 935854080 z^11 + 51572736 z^12 + 1458176 z^13 + 16384 z^14) BesselI[0, z/2]) + (1/(9282994875 z)) (4 E^(z/2) (-456080625 - 516891375 z + 2483289900 z^2 - 3564615600 z^3 + 3902320800 z^4 - 4254314400 z^5 + 5621011200 z^6 - 11849535360 z^7 + 96180099840 z^8 + 109944679680 z^9 + 43936527360 z^10 + 8520960000 z^11 + 886419456 z^12 + 50139136 z^13 + 1441792 z^14 + 16384 z^15) BesselI[1, z/2])

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]