Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1331)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=5

http://functions.wolfram.com/07.22.03.1331.01

Input Form

HypergeometricPFQ[{-(7/2)}, {5, 11/2}, z] == (1/(29520691200 z^4)) (4 (2 z (18561921525 + 20317178700 z + 10930626000 z^2 + 9853905600 z^3 - 3277113600 z^4 + 196543488 z^5 - 3444736 z^6 + 16384 z^7) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (29674526175 + 26632122300 z + 13721626800 z^2 + 8372548800 z^3 - 3181781760 z^4 + 194835456 z^5 - 3436544 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]]) - Pi (22347950625 + 102162060000 z + 95351256000 z^2 + 50854003200 z^3 + 36324288000 z^4 - 12915302400 z^5 + 782745600 z^6 - 13762560 z^7 + 65536 z^8) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (22347950625 + 102162060000 z + 95351256000 z^2 + 50854003200 z^3 + 36324288000 z^4 - 12915302400 z^5 + 782745600 z^6 - 13762560 z^7 + 65536 z^8) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</apply> <cn type='integer'> 22347950625 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> StruveL </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]