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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(11/2), 4}, z] == (1/(343814625 z)) (4 E^(z/2) (103378275 + 57068550 z - 121621500 z^2 + 109317600 z^3 - 85730400 z^4 + 74934720 z^5 - 92655360 z^6 + 297907200 z^7 + 807909120 z^8 + 441914880 z^9 + 97287168 z^10 + 9977856 z^11 + 471040 z^12 + 8192 z^13) BesselI[0, z/2]) + (1/(343814625 z^2)) (4 E^(z/2) (-413513100 + 115540425 z - 85135050 z^2 + 88508700 z^3 - 71215200 z^4 + 52708320 z^5 - 42154560 z^6 + 42888960 z^7 - 72161280 z^8 + 485479680 z^9 + 358245888 z^10 + 87991296 z^11 + 9519104 z^12 + 462848 z^13 + 8192 z^14) 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]