Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9671)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9671.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 21/4}, -z] == (Sqrt[Pi] z^(1/4) (7120171570446309375 - 15773918556065670000 z + 12463343056644480000 z^2 - 7158432935098368000 z^3 + 10106022967197696000 z^4 + 2566609007542272000 z^5 + 156440929983528960 z^6 + 3362814437621760 z^7 + 27174258081792 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-1859525538889701375 + 1324156289447376000 z - 679716325588608000 z^2 + 511234728947712000 z^3 + 151968671978618880 z^4 + 9586645967831040 z^5 + 208599515136000 z^6 + 1694364598272 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + 4 (657580753944576000 - 1258960307830792875 z + 914592944043979200 z^2 - 519330277509120000 z^3 + 605075768904499200 z^4 + 158661798378209280 z^5 + 9738835848069120 z^6 + 209859215622144 z^7 + 1697585823744 z^8 + 4294967296 z^9) Sin[2 Sqrt[z]]))/ (7664857047996825600 z^(9/2))

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,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]